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Dry-beans classification aims to determine the physical features of each class. This research classification was based on seven dry-bean categories: Barbunya, Bombay, Cali, Horoz, Dermason, Seker, and Sira. The data is 13,611, which contains information on 16 morphological features. The amount of data for each class needs to be balanced. Therefore, the research steps involve preprocessing by balancing the data using the Synthetic Minority Over-Sampling Technique (SMOTE). After carrying out balanced data, the classification process uses Stochastic Gradient Boosting Machines (SGBM). This method is a development of the Gradient Boosting Tree, which takes the best results from the boosting process. The test scenario consists of three models: imbalanced class, balanced class with SMOTE, and normalization using a min-max scaler. Testing also compares with other machine learning methods. The results show that testing using SMOTE and SGBM leads to the best results with an accuracy of 95.38%, precision of 95.46%, recall of 95.44%, and f1-score of 95.48%. [ABSTRACT FROM AUTHOR]

The progress of a disease can be analyzed using multistate models. These models focus on two key parameters of interest: the transition hazard and the state occupation probabilities. The state occupation probabilities have been consistently estimated by the Aalen-Johansen estimator. This estimator is particularly well-suited for handling censoring and benefits from the Markov assumption in the underlying stochastic process. In some cases, these estimators may lead to estimators with higher variability. To mitigate this issue we propose alternative estimators that incorporate a preliminary estimation approach. We introduce also practical estimation techniques for the state occupation probabilities, considering covariate measures. We explore the finite sample behavior of the estimators through simulations. An application to breast cancer is included. [ABSTRACT FROM AUTHOR]

The modification of the statistical equation KdV is considered. Cnoidal and soliton solutions are obtained under the assumption that black noise has an effect. Using the perturbation method and the Gauss copula, the equation is reduced to the form of a stochastic differential equation, which can be solved numerically with the stochastic the Wiener process. [ABSTRACT FROM AUTHOR]

In this paper, the mean square exponential convergence of semi-linear stochastic differential equations is proved by using quadratic Lyapunov function approach with stochastic process. Many theoretical rustles for convergence and mean square exponential convergence as well as mean square exponential stability of different stochastic differential systems using the necessary mathematical conditions have been proposed and supported with mathematical proofs and illustration. The presented approach provides a sufficient condition for stability of some classes of stochastic differential equations. The quadratic types of Lyapunov function gives an effective technique to ensure stable qualitative behavior to stochastic differential system in the present of system random uncertainty corresponding to Brownian motion perturbation. [ABSTRACT FROM AUTHOR]

In the article, stable recurrent algorithms have been developed that allow to increase the accuracy of the process of identification of dynamic control objects with a delay under the influence of random processes and disturbances. When solving such a problem, the input and output parameters measured data serve as initial data. Although the constant delay terms obey the linear law, their properties make the solution of the problem much more difficult. Based on the application of dynamic filtering methods and time-dependent identification methods, there should be sufficient a priori information to apply the known and experienced methods to the problem under consideration. [ABSTRACT FROM AUTHOR]

The aim of the work is to find the best accuracy using wireless sensor network for stochastic processes over the fuzzy logic algorithms using Innovative Energy Efficiency Technique. A total of samples (N=1251) are collected from datasets available in kaggle. The samples are divided into test data set and training data set and to find the accuracy rate and compare with stochastic processes and fuzzy logic algorithms. Result: The performance has been improved in terms of accuracy for the stochastic process algorithm with 99.23% while the fuzzy logic algorithm has shown an accuracy of 99.1% with G power value of 80% and threshold 0.05%, CI 95% mean and standard deviation. Conclusion: Based on the results achieved the stochastic process algorithm is better accuracy than the fuzzy logic algorithm using wireless sensor networks of the considered datasets. [ABSTRACT FROM AUTHOR]

In this paper the impact of sum of the times of waiting of jobs in a 2-machine n-job Flow-Shop Scheduling (FSS) problem has been discussed. The aim of the study is to discover the optimal or near optimal job sequence so that the sum of the times of waiting should be minimized. A heuristic algorithm is proposed to attain the objective. The proposed heuristic delivers a solution to the problems with special structures as well as with random processing times. The Weighted mean absolute errors (WMAE) generated after computational experiments validates that the algorithm delivers the fairly accurate optimal solutions. The WMAE acquired are less than 0.01 for FSS problem with special structures and less than 0.06 for FSS problems with random times of processing. Further with the upsurge in job size WMAE becomes significantly small. [ABSTRACT FROM AUTHOR]

The Non-Homogeneous Poisson Process has been used to determine the occurrence of COVID-19 in an area. Being a Stochastic Process of the Poisson distribution, it deals with the probability of rare events. Unlike the other distributions, including the Poisson distribution and the Homogeneous Poisson Process, the Non-Homogeneous Poisson Process incorporates the idea of having non-homogeneous intensities. In this paper, we apply the process of modelling the trend of COVID-19 cumulative data in Baguio City during Alert Level 1 from March 1, 2022 to May 31, 2022. As part of model fitting, the Linear Intensity Function and the Power Law Process were incorporated. Applying the Non-Homogeneous Poisson Process in determining the best fit for the data through the Markov Chain Monte Carlo algorithm, it concluded that the daily cumulative cases and daily cumulative recoveries follow the Linear Intensity Function. On the other hand, the daily cumulative death follows the Power Law Process. [ABSTRACT FROM AUTHOR]

The theory of stochastic processes is a branch of mathematics that studies random phenomena in the dynamics of their development. It is a relatively new branch of probability theory, which has developed especially rapidly in recent decades in connection with the ever-expanding range of its practical applications. Different undergraduate educational programs include this course in the curricula of students training. Students studying stochastic processes should get a holistic view of the subject, skills, and abilities to apply models of random processes in their professional activity correctly and meaningfully. Therefore, when organizing the educational process in the discipline, the teacher must decide on the forms, means, and methods of teaching. The authors offer two approaches to the study of the "time series" section. To implement time series forecasting methods, students perform laboratory work that is performed in the Excel environment. The purpose of the laboratory work is the acquisition by students of practical skills for solving the tasks. [ABSTRACT FROM AUTHOR]

In today's difficult economic environment, many industrial enterprises are striving to minimize production costs, which include the cost of domestic transport services. The purpose of this article is to present a new approach to the organization of internal transport services for industrial enterprises, using the example of mining and processing, in presence of a stochastic nature of the extraction and processing of raw materials. In the article, transport services are considered on the example of an economic entity that is engaged in extraction and processing of marble. Various random processes are determined in the mode of operation of an industrial enterprise. A method for calculating the departure rhythms is offered, which ensures the uniform arrival of raw materials to plants, considering the parameters of the transport network. The problem of transport service of a mining and processing enterprise is formulated considering the stochastic nature of its work. [ABSTRACT FROM AUTHOR]

We consider two-type branching stochastic processes with offspring distributions from the power series distribution family. The estimation of the individual parameters is an important part of the statistical inference for branching processes. Models of estimation of multitype branching processes require a large amount of data that cannot always be observed and the the size of the population is often insufficient. The use of approximation methods like the machine learning approach to parameter estimation, allows us to obtain an algorithmic estimation in the presence of hidden data. This gives us a motivation to approach the parametric statistical estimation in the multitype branching setting using machine learning algorithms. We consider a Hamiltonian Monte Carlo algorithm to algorithmically estimate the parameters of the individual distribution of a two-type branching process and compare it to the Gibbs sampler. As a special case we consider the branching process with a multivariate Poisson offspring distribution. Examples are provided, as well as a software implementation, illustrated by simulations and computational results in Python. [ABSTRACT FROM AUTHOR]

This paper runs over regions where it approaches a lot of individual conduct information. This information can be useful to arrange the personality traits as per attribute received. In this paper, the framework proposes a mechanism have been studied the different type of personality attributes and do compose as per the best five super attributes so that under 5 personality traits covers all attributes as subset of all 5 developed personality traits. The framework utilizes learning calculations like Naive Bayes, j48, Decision tree and Random Forest alongside cutting-edge information mining to mine user attributes information and gain from the examples. This learning would now be able to be utilized to group/anticipate user identity in view of past orders. In this paper we have done the personality classification and our target audience are the students who want to know what kind of career path will be most appropriate for them. We have collected the data from students and then processed to classify their personality on the basis of that data. By using it will be very helpful to all students who don't know which career line are suitable for them? According to the output of this process Random Forest got the higher accuracy i.e., the personality traits of a particular individual we can suggest them a suitable career path based on the result. [ABSTRACT FROM AUTHOR]

The complex interaction of the spindle group parts during operation gives reason to consider the spindle run-out as a stationary random process. Four diagnostic groups of runout curve sweeps by frequency components are distinguished. The discrete Fourier transform (DFT) apparatus and the specially developed software module "DTFourier" are used for the analysis. The non-contact optical scheme of measuring the spindle movement due to the laser ray modulation by the edge of the grinding mandrel allows to measure both in statics and in dynamics with the application of working loads. The technique was tested on the data of recording the run-out of the spindle of the machine tool model 16K20T1. A discrete Fourier analysis of the spindle run-out curve made it possible to fully diagnose the run-out quality of the assembly and the effect of individual errors on the accuracy and quality of machining during longitudinal sharpening. [ABSTRACT FROM AUTHOR]

Paper is devoted to modeling the spread of viral infection in a small group of people. As a result of the chaotic movement of group members with infected people, the local concentration of virions increases. Exceeding the concentration of virions in the atmosphere above the critical value can lead to infection of susceptible members of the group. Our model consists of two parts. In the first part, we simulate the random movement of people in a confined space. The model is based on the theory of random processes and takes into account the collisions of people with each other and with obstacles. We consider panic as an increase in the amplitude of the chaotic velocity of individuals. Panic leads to an increase in the evacuation time from a limited space, and to an increase in the concentration of people. The appearance of a zone with an increased concentration of people leads to an increase in the concentration of virions in the local atmosphere. The second part of our study is devoted to modeling the growth of the COVID-19 pathogen concentration in the body of any person. We have modified the traditional COVID-19 pathogenic cell growth model. As a result of the transport of virions absorbed into the lungs of an individual, viral cells enter the area of the body where they are intensively replicated. We introduced the degree of initial immunity of the body and the critical concentration of virions, starting from which explosive replication of pathogen cells from infected cells of the body occurs. The presentation provides an illustration of the effect of initial immunity on the dynamics of infection. It is shown how medical intervention increases the degree of immunity and minimizes damage to body cells. Based on direct numerical simulation of infection in an atmosphere with a random concentration of virions, a fundamental difference in the dynamics of infection in a deterministic and random atmosphere is shown. [ABSTRACT FROM AUTHOR]

The sciences of matter embrace a number of disciplines closely concerning the world around us. Since our world is subject to continuous change, virtually every new undertaking or insight invites to a revised approach, beginning with the simplest chemical changes in homogeneous solutions. Mathematical models usually resort to stochastic processes to deal with chemical conversions taking intermediates and branched reactions into account. The main mathematical problem lies in meaningfully linearizing the equations ruling the reactions. However, catalysis, electro-, and photochemistry can lend themselves to outperformance with respect to changes occurring in the near-linear range. Dealing with the problem of increasing reaction or power yield beyond the linear regime lies outside thermodynamics, at least inasmuch as it becomes a nonlinear problem, that can only be solved in a small region around a given operating point. We expect a significant increase of the yield of a process above the value established by the energy conservation principle to break thermodynamics. Predictive models using probability theory, too, cease to be valid beyond the linear range, so that mechanical statistical methods aren't so good. Finally, computational modeling of selective and specific processes by a systematic refinement that includes each property of the phenomenon is prohibitively complicated. As an alternative, signal reception techniques could be employed to monitor signals associated to those processes, and possibly to control the latter. While processes are highly nonlinear, if a linear signal response can be adjusted to fit the produced change in yield, the process at stake can be followed experimentally, and modeled by suitably parametrizing the linear response. Mathematical models of the signal changes can assist more general insights and heuristic guesses. Faraday's investigations on electrolysis can be viewed as a first failed effort in this direction. On the one hand, in Faraday's time circuit design was not as advanced as today, and on the other, his approach lends itself to open a more general avenue in the understanding of selective and specific processes. Hence, I try and put the discovery of electrolysis in context. [ABSTRACT FROM AUTHOR]

In this paper we analyzed a M/M/1/N queue attains its capacity in time t. The customers are arrived according to the Poisson distribution with rate λ and are served on FCFS basis with rate µ. When the catastrophe occurs, all the customers in the system are wiped out completely. Then the system takes time to accept new customer which is restoration. The catastrophe occurs at the rate ξ and restoration with rate β. The probability vectors are derived using Matrix Geometric Approach for this model. By introducing the Random Processes {M (t), N (t); t ≥ 0}, some system performance measures are obtained using particular parameter. [ABSTRACT FROM AUTHOR]

We are concerned with a subclass of piecewise-deterministic Markov processes (PDMPs) that evolve on a Polish space through random jumps at exponentially distributed time intervals, while the behaviour between jumps is governed by a finite collection of flows, selected randomly at the jump times. The main goal of this paper is to provide a set of conditions sufficient for the exponential ergodicity of the corresponding transition semigroup in terms of the bounded Lipschitz distance. [ABSTRACT FROM AUTHOR]

In this paper, we bring a comparison study between the original genome sequence of SARS-CoV 2 virus, ID: MN908947, coming from China 2019, and sequences of SARS-CoV 2 virus - P.1 variant, coming from Brazil 2021. Using tools of stochastic processes and through the identification of each sequence as being a sample of a stochastic process, after finding the best model for each sequence, we build dendrograms using a metric introduced in [1] that show that the original sequence can be considered in a separated cluster when compared with the P.1 variant. [ABSTRACT FROM AUTHOR]

Petri Nets have been recognised as a powerful tool for modelling and analysis of discrete event systems. For complicated dynamical systems with many interdependent components, stochastic discrete event models such as Markov models or Stochastic Petri Nets are commonly used (SPN). Such a model is mathematically sound and can be used to carry out either analytical or numerical simulations. The time-dependent token flow for each place in the model, as well as the firing frequency of each transition, is determined via stochastic simulation of the network's time-dependent dynamic behaviour. Steady-state behaviour values of Continuous Time Markov Chain (CTMC) can be used for performance analysis. The scope of this paper pertains to the analysis of the stochastic marking process of the net based on CTMC, a semi-Markov Chain and a generalised semi-Markov process. [ABSTRACT FROM AUTHOR]

Markov Chain is a stochastic process that shows a sequence of events with the probability of an event depending on the probability of the previous event. The Markov Chain method can be applied to the daily data of Covid-19 cases due to the appropriate character between them. The purposes of this study were to analyze the data and obtain the transition probabilities of the risk level of Covid-19 cases from one step to another until the steady state conditions. The data was analyzed from 4thAugust 2020 to 9thMarch 2021 for suspect-probable and confirm-death categories of Covid-19 and it was collected from the official website of the Ogan Ilir Regency. The conditions of daily cases were identified as three conditions or states, namely decreasing state, constant state, and increasing state. The results for the suspect-probable case category data showed that the transition probabilities for the decreasing state was 0.0046, the constant state was0.9970, and the increasing was 0.0018. Based on these results, the largest transition probability was in the constant state. The category of confirm-death cases had only two states namely the constant state and the increasing state. The largest transition probability was in the constant state, which was 0.9493. These results mean that Covid-19 in the Ogan Ilir Regency based on the observed data for suspect-probable and confirm-death categories tend to be in the constant state. The daily cases were not increase or decrease. [ABSTRACT FROM AUTHOR]

In this paper we study estimator of mean residual life function in a partıally informatıve regression model, when life times are randomly censored on the right. We prove an asymptotic normality of estimators and the weakly convergence of a stochastic process to a Gaussian process in Skorohod space. [ABSTRACT FROM AUTHOR]

The analysis of the results of running dynamic tests of rigid compartment passenger cars that have undergone modernization with the extension of the service life. It has been established that the process of changing the coefficient of vertical dynamics over time is a random process with a pronounced sinusoidal component It has been determined that the random processes that characterize the coefficient of vertical dynamics are distributed according to the normal law. Correlation functions were constructed according to the results of the experiment for each of the modes of motion is proved that for the approximation of correlation functions it is expedient to use dependences in the form of damped cosine waves. For each of the driving modes, parameters have been determined that characterize. The results obtained make it possible to assess the residual life of modernized passenger cars with greater accuracy. [ABSTRACT FROM AUTHOR]

Intermodal transportations are the result of the interaction of a large number of counterparties and therefore represent a complex stochastic process. In the process, there is inconsistency in action and a degree of uncertainty that results in delays in transporting containers and associated additional costs. In order to establish the technological process of container transportation by rail and interaction with the port in the organization of intermodal transportation, the article examines the flow of container flows to one of the railway terminal stations. It is proved that the container flows coming from shippers to the station have signs of stochasticity and belong to non-stationary, extraordinary Poisson flows. [ABSTRACT FROM AUTHOR]

The Geometric Brownian Motion (GBM) model assumes that asset log returns are normally distributed. In fact, many asset log returns are found that are not normally distributed, therefore another model is needed, one of them is the Variance Gamma (VG) model. The VG process is a stochastic process. This process has three parameters which are generalizations of the Brownian motion that developed the Brownian. The added parameters are the drift of Brownian motion and the volatility of time changes. The VG process is used for modeling asset log returnsAs well as the GBM model, the VG model is widely applied in stock price modeling. Theoretically, the movement of the stock price of one company will be followed by the movement of the stock price of another company. Therefore, it would be more appropriate if the modeling was carried out together, namely using the Multivariate Variance Gamma (MVG) model. In this study, the Bivariate Variance Gamma (BVG) model was used. The data used is the daily closing price of stock of PT Bank Rakyat Indonesia (Persero) Tbk and PT Bank Negara Indonesia (Persero) Tbk. The parameter estimation was carried out using the maximum likelihood approach. Meanwhile, stock price prediction was carried out by using a Monte Carlo simulation approach. In this study, the prediction results using BVG obtained MAPE value less than10% which concludes that forecasting accuracy is excellent. [ABSTRACT FROM AUTHOR]

The article deals with the problem of ensuring the safety of processes related to the functioning of technical systems, the movement of vehicles, the operation of infrastructure on the example of railway transport. The analysis and forecasting of extreme modes leading to the occurrence of dangerous accidents in transport is carried out using probabilistic modeling of random processes in technical systems. In order to build models, the normal and logarithmically normal distributions of the studied characteristics were used, which are in good agreement with the observed statistics for the analyzed random variables. According to the proposed method, the problem of exceeding the permissible level of condensation pressure in heat exchangers of refrigerated rolling stock is taken into account. Recommendations for improving the safety of maintenance of refrigerated sections are given. The problem of ensuring the safe crossing of railway tracks by a team of workers is considered. Taking into account the data of statistical studies, the probabilistic and time indicators of the exit of a team of workers from a dangerous zone are calculated. The developed methodology for probabilistic modeling of transport processes is recommended for analyzing and predicting the risks of dangerous events and ensuring railway transport safety. [ABSTRACT FROM AUTHOR]

A stochastic model of an information channel with random intensities and random loads is constructed. We investigate a model of an information flow in which some part of information from "the past" is projected to "the present" and another part of the information is left behind. The "present" information is supplemented by some innovations which replace the vanished information. We obtain several limit theorems for normed sums of independent identically distributed information channels. A class of limit processes consists of various generalizations of the Ornstein–Uhlenbeck process. We also describe a construction of self-similar processes with a wide range of one-dimensional distributions of their truncations. [ABSTRACT FROM AUTHOR]

A lot of mechanical oscillating systems have nonlinearity which cannot be neglected. A Duffing oscillator can successfully approximate the nonlinearity present in a majority of oscillating mechanic systems. When driven with a periodic force it may respond with motion having single or multiple periodicities or may even display chaotic behaviour depending on the strength of the driving force. The response could range from a simple harmonic motion to complex chaotic trajectories. This complexity in the response of a driven Duffing oscillator is studied independently using both classical and quantum models which are used to investigate stochastic process. Regions in the bifurcation diagram with single and multiple periodicity and chaotic behaviour can be distinguished using both algorithms. Further, both algorithms show variation in their output within the chaotic range indicating that all chaotic time series may not be same in terms of their complexity. [ABSTRACT FROM AUTHOR]

An optimal economic Statistical Process Control (SPC) scheme comprising Shewhart X chart and Exponentially Weighted Moving Average (EWMA) chart (known as economic combined Shewhart-EWMA chart) is developed based on random process shifts for monitoring process mean. The proposed model minimizes the total cost associated with the charting scheme under the constraints of false signal and inspection rates. The performance (in terms of total associated cost) of the proposed economic combined Shewhart-EWMA chart is compared with that of an optimal economic single X̅ chart and an optimal economic single EWMA chart. The results show that the optimal economic combined Shewhart-EWMA chart reduces the associated cost by about 40% and 13.6%, compared to the optimal economic single X̅ chart and the optimal economic single EWMA chart, respectively. [ABSTRACT FROM AUTHOR]

Models of stochastic processes describe many phenomena in nature, technology, and economics. However, STEM and economics students usually do not have enough time to study this topic. When developing a course on stochastic processes, a teacher faces some challenges. The task is to present sophisticated educational material, combining the mathematical severity of presentation and ease of understanding. Throughout several lessons, students should get a holistic understanding of the subject so that they can correctly and meaningfully apply models of stochastic processes in the field of their professional activities. The complicated nature of stochastic processes models requires understanding their multidimensionality, facilitated by various representation methods: formulas, tables, graphs, and computer simulation. The article discusses applying these techniques on the example of the formation of the concepts "stochastic process" "mathematical expectation and variance of a stochastic process." [ABSTRACT FROM AUTHOR]

Glucagon –like peptide 1 (GLP-1) is a hormone it stimulate to decrease in blood glucose levels and it is used for the type2 diabetes treatment. In this GLP-1 insulin secretion, the effects of β-cell are important to indentify. During the intake of glucose only the effects of β-cell in Glucagon-like peptide 1 have been identify the distinctive nature in humans, but not in intake like meal, are not identify. [ABSTRACT FROM AUTHOR]

A k-out-of-n system reliability is being investigated in which all components have identical characteristics and are exposed to dependent failure processes degradation and random shock stress. In this paper, we look at two competing failures are nonfatal due to gradual degradation and the sudden increment in the degradation caused by random shocks and catastrophic failures caused by the same shock processes. Each component can fail due to extreme shock damage or total degradation exceeds the critical thresholds. The time-to-failure for all the components are probabilistically dependent. All the components are affected by both failure processes. The failure processes are mutually dependent since any one of process can cause the component to fail. The system works if only if at least k of its n components is functioning. A numerical illustration is given to demonstrate the proposed method. [ABSTRACT FROM AUTHOR]

A new stochastic framework for parameter estimation and uncertainty quantification in colon cancer-induced immune response is presented. The dynamics of colon cancer is given by a stochastic process that captures the inherent randomness in the system. The stochastic framework is based on the Fokker-Planck equation that represents the evolution of the probability density function corresponding to the stochastic process. An optimization problem is formulated that takes input individual patient data with randomness present, and is solved to obtain the unknown parameters corresponding to the individual tumor characteristics. Furthermore, sensitivity analysis of the optimal parameter set is performed to determine the parameters that need to be controlled, thus, providing information of the type of drugs that can be used for treatment. [ABSTRACT FROM AUTHOR]

In this paper we define a risk model with stochastic premium process, such that the counting processes are not independent. We consider a special case of bivariate counting process. Then we derive equations for the non-ruin probability in infinite time and analyze the case of exponentially distributed claims. [ABSTRACT FROM AUTHOR]

A piecewise deterministic Markov process with random switching between flows, occuring e.g. in certain stochastic models for gene expression, is considered in this article. The main goal is to provide a set of reasonable conditions under which any stationary distribution of the process that corresponds to an ergodic stationary distribution of the discrete-time Markov chain given by the post-jump locations of this process has a density with respect to the Lebesgue measure. [ABSTRACT FROM AUTHOR]

A scheme combining the classical method of steps with expansion of the state space (MSSSE) was earlier proposed for an analysis of systems of stochastic ordinary differential equations with one constant time delay (SODDEs). This two-stage scheme is adapted for the analysis of new models described by stochastic partial differential equations (SPDEs) with delays (SPDDEs). The modified scheme together with a usage of the generalized Fokker–Planck– Kolmogorov equation (FPK Eq.) for the probability density functional makes it possible to construct a chain of SPDEs without delays. We exploit this chain to obtain new sequence of PDEs for calculating the first moment functions (fields) of the solution on successive time intervals. Some results of symbolic and numeric calculations for parabolic and hyperbolic equations that carried out in the environment of the mathematical package Mathematica, are presented. [ABSTRACT FROM AUTHOR]

Consider a convex hull generated by a homogeneous Poisson point process in a cone on the plane. In this paper, we present a result that the area of bounded perimeters of the convex hull and the support boundary of the distribution in the cone is the sum of independent identically distributed random variables. In addition, we prove the central limit theorem for the number of vertices of the convex hull in a cone bounded by a disk of radius T as T → ∞. The known results of [1] coincide with the results obtained in the paper. [ABSTRACT FROM AUTHOR]

In this paper that the estimate of the convergence rate of the remainder term in the main lemma of the theory of Galton-Watson critical branching random processes is of order O ( ln n n) , n → ∞ is proved. [ABSTRACT FROM AUTHOR]

The paper proposes a method for determining of an aircraft wing thermal state during flight in icing conditions. The method is based on a probabilistic representation of a boundary value problem for a parabolic type equation and numerical solution of stochastic differential equations. It is assumed that the heat exchange process in a problem of the type under consideration is described quite well by the boundary value problem for the two-dimensional heat equation. The approximate solution definition at a given point is reduced to the numerical simulation of the diffusion random process paths. [ABSTRACT FROM AUTHOR]

LQ45 is one of many Indeks Harga Saham (IHS) which is included in Bursa Efek Indonesia (BEI). IHS is used by investors to predict the stock prices. The motion of IHS is unpredictable causes the investors in quandary situation. Stochastic model is probabilistic model based on an event which is characterized with parameters value and time-variant. IHS fluctuate causes unpredictable effect that is also the feature of stochastic process. The uncertainty can be measured by fuzzy then the composite of both is fuzzy stochastic. On fuzzy, membership value used as parameter approach is fuzzy linguistic summary (FLS). FLS has not examined chance of fluctuation the stock prices motion, so that Markov chain's combination is used as the approach of parameter r. The r parameter has five state, those are the steady, rising, most rising, falling, and most falling. There are three kinds of stocks return, which are the positive return, negative return, and no return. The clustering process uses fuzzy c-means results the positive return clusters and negative return clusters. This research results interval on five sorted interval clusters −5.17 ≤ x ≤ 1.17 when IHS is most falling, −1.17 < x < 0 when IHS is falling, 0 when IHS is steady, 0 < x < 1.2 when IHS is rising, dan 1.2 ≤ x ≤ 3.73 when IHS is most rising and stochastic model obtained is X (n + 1) = X (n)er along r is the parameter of five states, rsteady = 0, 0001, rrising = 0, 0106, rmostrising = 0, 0135, rfalling = 0, 0072 and rmost falling = 0, 0104. The fuzzy stochastic model with those parameters on five states has MAPE value 0,49% therefore the model has great forecasting capability. [ABSTRACT FROM AUTHOR]

Caputo fractional differential equations of order q ∈ (1, 2) with impulses at random moments are set up and investigated in this paper. The main characteristic of the studied equations is that the impulses occur at random moments which are exponentially distributed random variables. It leads to a total change of the behavior of the solution which is a stochastic process. Also, we assume at the moments of impulses the lower limit of Caputo fractional derivative is changed. The initial value problem is set up in appropriate way. Sample path solutions are defined as a solutions of Caputo fractional differential equations with determined fixed moments of impulses. P-moment exponential stability is defined and some sufficient conditions for this type of stability are obtained. The study is based on the application of Lyapunov functions and the appropriate its Caputo fractional derivative among the studied fractional equation. [ABSTRACT FROM AUTHOR]

We report an experimental and theoretical analysis of the phase switch from the zero voltage state to the finite voltage state of Bi2Sr2CaCu2Oy intrinsic Josephson junctions (IJJs). In the resistively and capacitively shunted junction (RCSJ) model for a single Josephson junction, the effect of thermal fluctuations is taken into account as two stochastic processes: the thermally activated (TA) escape process from a potential well and the phase retrapping (PR) process to the next potential well. The two different methods examined here are (i) the so-called TA+PR model, which considers only successive PR processes after the TA escape process and (ii) the Monte Carlo simulations, which numerically simulate the sequence of stochastic processes. The fitting of the experimental data based on those two methods indicate that the complex stochastic processes missing in the TA+PR model are needed to explain the switching current distribution at relatively high temperatures. Furthermore, we propose the multi- RCSJ model taking into account a layered crystal structure of IJJs, and demonstrate the validity through a detailed fitting with experimental data. [ABSTRACT FROM AUTHOR]

A new Fokker-Planck control framework is presented to control the spread and flow of traffic motion that is modeled using a stochastic process. This framework is based on the minimization of an expectation functional subject to a Fokker-Planck equation that models the evolution of the probability density function of the underlying stochastic process. The Fokker-Planck equation comprises of sparse bilinear optimal controls for the flow and spread of the stochastic process. Theoretical results on existence of optimal controls was derived. A new and efficient scheme for solving the Fokker-Planck equation was also presented that is conservative, positive, stable, second order accurate, that can be easily extended to higher dimensions. Numerical results of controlled motion of traffic along trajectories containing obstacles demonstrated the effectiveness of the proposed framework. [ABSTRACT FROM AUTHOR]

Branching processes form an important and wide subclass of stochastic processes. They have numerous applications in different scientific and practical areas, from biology and cell proliferation through epidemiology, physics and neutral chain reactions to finance and insurance. Many of them involve multitype modeling. Statistical estimation of the process' characteristics is an important issue in their study. The nature of the models require a big amount of data, which is often impossible to be observed, considering only the total population sizes. In order to obtain the maximum likelihood estimators when the information is not sufficient, we use approximation methods. In our study the EM algorithm serves as an effective instrument for calculation of the estimates when a part of data is hidden. We propose examples of two-type branching processes with multinomial offspring distributions and a software implementation of the EM algorithm, illustrated via simulations and computational results. [ABSTRACT FROM AUTHOR]

The paper deals with the modeling of structural patterns characterized by unilateral conditions when some uncertainty occurs. This is the case, for example, when an elastic beam lies on a rigid soil whose profile is unknown and needs some modeling through the recourse to a random process. The topic has been previously treated by the authors and the present paper refers to the developed researches, addressing the case of beams discretized into a number of finite beam-elements, and assuming as significant only the ordinates of the soil profile under the nodal points. Energetic properties of the solution are demonstrated to hold, which are shown to represent the premise for the whole treatment, since they allow to set the fundamental complementarity relation ruling the problem. [ABSTRACT FROM AUTHOR]

In this paper, we develop a model selection procedure for paired stochastic processes (Yt, Xt) where the Markov chain Xt chooses the set of transition probabilities to be used by Yt at time t. More precisely Xt is an order p Markov chain and given the value of Xt at time t, the (response) process Yt is an order o Markov chain with transition probabilities that depend on the specific value of Xt. This situation is different from Hidden Markov models and Double Markov chains (see [1]) since in our case, both processes Xt and Yt are observed. We define a family of models for this situation and investigate a consistent model selection procedure such that the final model has a minimal number of parameters. The methodology used to select a model is based on the Bayesian Information Criterion (BIC) by Schwarz [2]. The procedure consists of finding a partition of the joint state space determining the relationship between the joint processes of covariate and the response. The model and the model selection methodology, itroduced here, are generalizations of the Partition Markov models by Garćıa and González-López [3], [4], [5], and [6]. [ABSTRACT FROM AUTHOR]

In this study, the temporal fluctuation of the speed of a vehicle plying in traffic is modelled as a stochastic process with an exponentially decaying memory function. Results of the stochastic modeling are compared with simulations using a two-lane Nagel-Schreckenberg cellular automata traffic model for speeds involving different traffic scenarios. Vehicular speeds were also obtained from the position of actual vehicles in real-world scenarios using a Global Positioning System (GPS) data logger which records the position with one second time interval. The mean squared displacements (MSD) of the speed's temporal fluctuation for both the simulation and the GPS data match the theoretical MSD given by, MSD(T) = C(1−e−T/Tc). The simulation confirms that the values of the two parameters, Tc and C, of the MSD indicate sensitivity to the different vehicular densities. The time constant Tc decreases as the density increases while the relation between C and density shows a similar behavior to that of the traffic flow-density relation where two traffic regimes can be clearly defined. The dependence of the parameters to the vehicular density allows the stochastic model to determine the density and flow at any section of the road in real-time. The stochastic model of a single vehicle's speed fluctuation is especially useful in traffic forecasting and management since this enables the gathering of essential traffic data with high spatial and temporal resolution. [ABSTRACT FROM AUTHOR]

The link between Markovian and non-Markovian stochastic processes is examined by looking at the drift and diffusion coefficients. Starting with the Langevin equation, a solution for the Fokker-Planck equation is obtained using white noise analysis. An evaluation of the mean square displacement explicitly shows that the drift coefficient may not play a crucial role in transitions from Markovian to non-Markovian processes. A special case of the solution obtained for the Fokker-Planck equation is fractional Brownian motion which we use to consider absorbing boundaries. [ABSTRACT FROM AUTHOR]

The generalized grey Brownian motion is a time continuous self-similar with stationary increments stochastic process whose one dimensional distributions are the fundamental solutions of a stretched time fractional differential equation. Moreover, the distribution of the time-changed Brownian motion by an inverse stable process solves the same equation, hence both processes have the same one dimensional distribution. In this paper we show the mutual singularity of the probability measures on the path space which are induced by generalized grey Brownian motion and the time-changed Brownian motion though they have the same one dimensional distribution. This singularity property propagates to the probability measures of the processes which are solutions to the stochastic differential equations driven by these processes. [ABSTRACT FROM AUTHOR]

In this paper, an analysis of the performance of Engineering students of Professional College in Coimbatore District has been done using the concept of Absorbing Markov Chain. The study has been carried out to assess various performance attributes of the learners of engineering stream. The outcomes of four programmes offered by an Engineering College for eight semesters in four years have been studied and it has been attempted to arrive out the mean value of the time used-up by the students during a semester, total semesters taken to get the graduation on completion and the probability of a student getting graduated from the institution or withdrawn from the course. [ABSTRACT FROM AUTHOR]

Evaporative assembly of colloids in tiny contact free droplet is a facile and one step process to realize nanostructured microgranules. In such a process, with relatively fast drying rate a random jamming of the nanoparticles are expected. Here we have shown that even in such a rapid random jamming process, a nice local hexagonal ordering can exist. Although the local volume fraction of the nanoparticles in the granules is not affected in a statistically sense, the intermediate range ordering gets influenced depending on the rapidness of the assembly process. [ABSTRACT FROM AUTHOR]