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This article deals with the emergence of a specific mating preference pattern called homogamy in a population. Individuals are characterized by their genotype at two haploid loci, and the population dynamics is modelled by a nonlinear birth-and-death process. The first locus codes for a phenotype, while the second locus codes for homogamy defined with respect to the first locus: two individuals are more (resp. less) likely to reproduce with each other if they carry the same (resp. a different) trait at the first locus. Initial resident individuals do not feature homogamy, and we are interested in the probability and time of invasion of a mutant presenting this characteristic under a large population assumption. To this aim, we study the trajectory of the birth-and-death process during three phases: growth of the mutant, coexistence of the two types, and extinction of the resident. We couple the birth-and-death process with simpler processes, like multidimensional branching processes or dynamical systems, and study the latter ones in order to control the trajectory and duration of each phase. [ABSTRACT FROM AUTHOR]

We prove under mild conditions that the Fleming-Viot process selects the minimal quasi-stationary distribution for Markov processes with soft killing on non-compact state spaces. Our results are applied to multi-dimensional birth and death processes, continuous time Galton-Watson processes and diffusion processes with soft killing. [ABSTRACT FROM AUTHOR]

The signs of deterioration in worldwide infrastructure and the associated socio-economic and environmental losses call for sustainable resource management and policy-making. To this end, this work presents an enhanced variant of partially observable Markov decision processes (POMDPs) for the life cycle assessment and maintenance planning of infrastructure. POMDPs comprise a method, commonly employed in the field of robotics, for decision-making on the basis of uncertain observations. In the work presented herein, a continuous-state POMDP formulation is presented which is adapted to the problem of decision-making for optimal management of civil structures. The aforementioned problem may comprise non-linear and non-deterministic action and observation models. The continuous-state POMDP is herein coupled with a normalised unscented transform (NUT) in order to deliver a framework able to tackle non-linearities that likely characterise action models. The capabilities of this enhanced framework and its applicability to the maintenance planning problem are presented via two applications. In a first illustrative example, the use of the NUT is demonstrated within the framework of the value iteration algorithm. Next, the proposed continuous-state framework is compared against a discrete-state formulation for implementation on a life cycle assessment problem. [ABSTRACT FROM PUBLISHER]

In this paper, we obtain a general achievable rate region for discrete memoryless multiple-access relay channel (DM-MARC) with common message via partial decode and forward strategy and regular block Markov encoding/backward decoding. This general achievable rate region, as an extension of the achievability part of the relay channel via partial decode and forward strategy to the MARC, subsumes the previous known achievable rate regions for multiple-access channel with common message and MARC. Also, by applying Fano's inequality, we derive an outer bound for DM-MARC with common message. By extending the discrete alphabet results to the continuous alphabet, an inner bound for Gaussian MARC (GMARC) is achieved. As expected, our results for the Gaussian MARC includes the previous results for the Gaussian multiple-access channel with and without common message and the Gaussian relay channel as special cases. Finally, by considering a specific topology for MARC, performance of GMARC with common message versus the position of the relay is investigated numerically. Also, it is shown that our achievable rate region is larger than the previous rate region of GMARC with common message with irregular encoding/successive decoding. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In an M/ M/1/ C queue, customers are lost when they arrive to find C customers already present. Assuming that each arriving customer brings a certain amount of revenue, we are interested in calculating the value of an extra waiting place in terms of the expected amount of extra revenue that the queue will earn over a finite time horizon [0, t]. There are different ways of approaching this problem. One involves the derivation of Markov renewal equations, conditioning on the first instance at which the state of the queue changes; a second involves an elegant coupling argument; and a third involves expressing the value of capacity in terms of the entries of a transient analogue of the deviation matrix. In this paper, we shall compare and contrast these approaches and, in particular, use the coupling analysis to explain why the selling price of an extra unit of capacity remains the same when the arrival and service rates are interchanged when the queue starts at full capacity. [ABSTRACT FROM AUTHOR]

This paper deals with a single-server queue with modulated arrivals, service requirements and service capacity. In our first result, we derive the mean of the total workload assuming generally distributed service requirements and any service discipline which does not depend on the modulating environment. We then show that the workload is exponentially distributed under heavy-traffic scaling. In our second result, we focus on the discriminatory processor sharing (DPS) discipline. Assuming exponential, class-dependent service requirements, we show that the joint distribution of the queue lengths of different customer classes under DPS undergoes a state-space collapse when subject to heavy-traffic scaling. That is, the limiting distribution of the queue-length vector is shown to be exponential, times a deterministic vector. The distribution of the scaled workload, as derived for general service disciplines, is a key quantity in the proof of the state-space collapse. [ABSTRACT FROM AUTHOR]

This paper investigates the reliable mixed passive and [ABSTRACT FROM AUTHOR]

In collaborative wireless networks with low infrastructure, the presence of misbehaving nodes can have a negative impact on network performance. In particular, we are interested in dealing with this nasty presence in road safety applications, based on vehicular ad hoc networks (VANETs). In this paper, we consider as harmful the presence of malicious nodes, which spread false and forged data, and selfish nodes, which cooperate only for their own benefit. To deal with this, we propose a distributed trust model (DTM^2), which is adapted from the job market signaling model. DTM^2 is based on allocating credits to nodes and securely managing these credits. To motivate selfish nodes to cooperate more, our solution establishes the cost of reception to access data, forcing them to earn credits. Moreover, to detect and exclude malicious nodes, DTM^2 requires the cost of sending, using signaling values inspired from economics and based on the node's behavior so that the more malicious a node is, the higher its sending cost, thus limiting their participation in the network. Similarly, rewards are given to nodes whose sent messages are considered truthful and that paid a sending cost considered correct. The latter is a guarantee for the receivers about the truthfulness of the message since, in the case of message refusal, the source node is not rewarded, despite its payment. We validated DTM^2 via a theoretical study using Markov chains and with a set of simulations in both urban and highway scenarios. Both theoretical and simulation results show that DTM^2 excludes from the network 100% of malicious nodes without causing any false-positive detection. Moreover, our solution guarantees a good ratio of reception, even in the presence of selfish nodes. [ABSTRACT FROM PUBLISHER]

We extend to Markov-modulated Brownian motion (MMBM) the renewal approach which has been successfully applied to the analysis of Markov-modulated fluid models. It has been shown recently that MMBM may be expressed as the limit of a parameterized family of Markov-modulated fluid models. We prove that the weak convergence also holds for systems with two reflecting boundaries, one at zero and one at $$b >0$$ , and that the stationary distributions of the approximating fluid models converge to the stationary distribution of the two-sided reflected MMBM. In so doing, we obtain a new representation for the stationary distribution. It is factorised into a vector determined by the phase behaviour when the fluid is either at the level 0 or the level $$b$$ , and a matrix expression characteristic of the process when the fluid is in the open interval $$(0,b)$$ . [ABSTRACT FROM AUTHOR]

Two sequentially Markov coalescent models (SMC and SMC9) are available as tractable approximations to the ancestral recombination graph (ARG). We present a Markov process describing coalescence at two fixed points along a pair of sequences evolving under the SMC9. Using our Markov process, we derive a number of new quantities related to the pairwise SMC9, thereby analytically quantifying for the first time the similarity between the SMC and the ARG. We use our process to show that the joint distribution of pairwise coalescence times at recombination sites under the SMC is the same as it is marginally under the ARG, which demonstrates that the SMC is, in a particular well-defined, intuitive sense, the most appropriate first-order sequentially Markov approximation to the ARG. Finally, we use these results to show that population size estimates under the pairwise SMC are asymptotically biased, while under the pairwise SMC they are approximately asymptotically unbiased. [ABSTRACT FROM AUTHOR]

Autocorrelated data arise in a variety of processes. To statistically monitor such processes, special statistical tools are needed to account for these correlations. The most common set of tools for such purpose is the autoregressive integrated moving average (ARIMA) models. Implementation of ARIMA models requires a fair amount of background understanding of how these models work, because the model selection step is essential. In this paper, we propose a new monitoring technique based on the use of hidden Markov models. The proposed monitoring method is powerful yet simple to use technique because it only requires a basic knowledge in statistics. Simulation results show that the proposed method performs similar to the ARIMA models in terms of average run length for detecting out of control processes and false alarms. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

ABSTRACT We propose a new model for multivariate Markov chains of order one or higher on the basis of the mixture transition distribution (MTD) model. We call it the MTD-Probit. The proposed model presents two attractive features: it is completely free of constraints, thereby facilitating the estimation procedure, and it is more precise at estimating the transition probabilities of a multivariate or higher-order Markov chain than the standard MTD model. [ABSTRACT FROM AUTHOR]

The results of numerical modeling of the geomagnetic secular variation by the method of the Giant Gaussian Process (GGP) are presented and compared with the information derived from the presentday databases for paleointensity. The variances of the positions of the virtual geomagnetic pole (VGP) calculated from the synthetic and experimental data (Brunhes epoch, effusive rocks) are nearly similar, which supports the validity of the theoretical model. The average value of the virtual axial geomagnetic dipole (VADM) calculated from the PINT world database on paleointensity and the Sint-2000 model is lower than VADM calculated by the GGP model; at the same time, the estimates based on the archaeomagnetic data give the VADM value slightly above the model prediction. The largest difference is observed in the variances of VADM, which is for all the three databases noticeably higher than the value calculated from the GGP model. Most probably, this is due to the contribution of the neglected measurement errors of VADM. [ABSTRACT FROM AUTHOR]

For any branching process, we demonstrate that the typical total number rmp(vτ) of events triggered over all generations within any sufficiently large time window τ exhibits, at criticality, a superlinear dependence rmp(vτ) ~ (vτ)γ (with γ > 1) on the total number vτ of the immigrants arriving at the Poisson rate v. In branching processes in which immigrants (or sources) are characterized by fertilities distributed according to an asymptotic power-law tail with tail exponent 1 < γ < 2, the exponent of the superlinear law for rmp(vτ) is identical to the exponent y of the distribution of fertilities. For γ > 2 and for standard branching processes without power-law distribution of fertilities, rmp(vτ) ~ (vτ)². This scaling law replaces and tames the divergence vτ/(l -- n) of the mean total number Rt(τ) of events, as the branching ratio (defined as the average number of triggered events of first generation per source) tends to 1. The derivation uses the formalism of generating probability functions. The corresponding prediction is confirmed by numerical calculations, and an heuristic derivation enlightens its underlying mechanism. We also show that Rt(τ) is always linear in VT even at criticality (n = 1 ). Our results thus illustrate the fundamental difference between the mean total number, which is controlled by a few extremely rare realizations, and the typical behavior represented by rmp(vτ). [ABSTRACT FROM AUTHOR]

With the increase of product reliability, collecting time-to-failure data is becoming difficult, and degradation-based method has gained popularity. In this paper, a novel multi-hidden semi-Markov model is proposed to identify degradation and estimate remaining useful life of a system. Multiple fused features are used to describe the degradation process so as to improve the effectiveness and accuracy. The similarities of the features are depicted by a new variable combined with forward and backward variables to reduce computational effort. The degradation state is identified using modified Viterbi algorithm, in which linear function is adopted to describe the contribution of each feature to the state recognition. Subsequently, the remaining useful life can be forecasted by backward recursive equations. A case study is presented, and the results demonstrate the validity and effectiveness of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We consider a birth-death process with birth rates iλ and death rates iμ+ i( i−1) θ, where i is the current state of the process. A positive competition rate θ is assumed to be small. In the supercritical case where λ > μ, this process can be viewed as a demographic model for a population with high carrying capacity around ( λ−μ) /θ. The article reports in a self-contained manner on the asymptotic properties of the time to extinction for this logistic branching process as θ → 0. All three reproduction regimes λ > μ, λ < μ, and λ = μ are studied. [ABSTRACT FROM AUTHOR]

Markovian systems with multiple interacting subsystems under the influence of a control unit are considered. The state spaces of the subsystems are countably infinite, whereas that of the control unit is finite. A recent infinite level-dependent quasi-birth-and-death model for such systems is extended by facilitating the automatic representation and generation of the nonzero blocks in its underlying infinitesimal generator matrix with sums of Kronecker products. Experiments are performed on systems of stochastic chemical kinetics having two or more countably infinite state space subsystems. Results indicate that, even though more memory is consumed, there are many cases where a matrix-analytic solution coupled with Lyapunov theory yields a faster and more accurate steady-state measure compared to that obtained with simulation. [ABSTRACT FROM AUTHOR]

As a mathematical theory for the stochastic, nonlinear dynamics of individuals within a population, Delbrück-Gillespie process (DGP) is a birth-death system with state-dependent rates which contain the system size V as a natural parameter. For large V, it is intimately related to an autonomous, nonlinear ODE as well as a diffusion process. For nonlinear dynamical systems with multiple attractors, the quasi-stationary and stationary behavior of such a birth-death process can be understood in terms of a separation of time scales by a T*∼ eα V (α > 0): a relatively fast, intra-basin diffusion for t≪ T* and a much slower inter-basin Markov jump process for t≫ T*. In this paper for one-dimensional systems, we study both stationary behavior ( t=∞) in terms of invariant distribution , and finite time dynamics in terms of the mean first passsage time (MFPT) . We obtain an asymptotic expression of MFPT in terms of the 'stochastic potential'. We show in general no continuous diffusion process can provide asymptotically accurate representations for both the MFPT and the for a DGP. When n1 and n2 belong to two different basins of attraction, the MFPT yields the T*( V) in terms of Φ ( x, V) ≈φ0( x) + (1/ V)φ1( x). For systems with saddle-node bifurcations and catastrophe, discontinuous 'phase transition' emerges, which can be characterized by Φ ( x, V) in the limit of . In terms of timescale separation, the relation between deterministic local nonlinear bifurcations, and stochastic global phase transition is discussed. The one-dimensional theory is a pedagogic first step toward a general theory of DGP. [ABSTRACT FROM AUTHOR]

Abstract: We consider birth–death processes on the nonnegative integers, where is an irreducible class and 0 an absorbing state, with the additional feature that a transition to state 0 (killing) may occur from any state. Assuming that absorption at 0 is certain we are interested in additional conditions on the transition rates for the existence of a quasi-stationary distribution. Inspired by results of Kolb and Steinsaltz [M. Kolb, D. Steinsaltz, Quasilimiting behavior for one-dimensional diffusions with killing, Ann. Probab. 40 (2012) 162–212] we show that a quasi-stationary distribution exists if the decay rate of the process is positive and exceeds at most finitely many killing rates. If the decay rate is positive and smaller than at most finitely many killing rates then a quasi-stationary distribution exists if and only if the process one obtains by setting all killing rates equal to zero is recurrent. [Copyright &y& Elsevier]

Abstract: In this paper, we develop a stochastic process rules (SPR) based Markov chain method to calculate the degree distributions of evolving networks. This new approach overcomes two shortcomings of Shi, Chen and Liu’s use of the Markov chain method (Shi et al. 2005 ). In addition we show how an SPR-based Markov chain method can be effectively used to calculate degree distributions of random birth-and-death networks, which we believe to be novel. First SPR are introduced to replace traditional evolving rules (TR), making it possible to compute degree distributions in one sample space. Then the SPR-based Markov chain method is introduced and tested by using it to calculate two kinds of evolving network. Finally and most importantly, the SPR-based method is applied to the problem of calculating the degree distributions of random birth-and-death networks. [Copyright &y& Elsevier]

A Utensils formation system of utensils industry is analyzed for its availability. Birth and death equations governing the system are formed, taking constant failure and repair rates, using Markov method. These equations are solved using Matrix method. These equations are solved using Matrix method with the help of computer programme. The approaches are identified through availability analysis of utensils formation system of utensils industry which could help in improving its availability. Long run availability is studied with the help of tables and graphs. The results so obtained are useful for reliability engineers and the managers [ABSTRACT FROM AUTHOR]

This paper describes efficient procedures for model checking Markov reward models, that allow us to evaluate, among others, the performability of computer-communication systems. We present the logic CSRL (Continuous Stochastic Reward Logic) to specify performability measures. It provides flexibility in measure specification and paves the way for the numerical evaluation of a wide variety of performability measures. The formal measure specification in CSRL also often helps in reducing the size of the Markov reward models that need to be numerically analysed. The paper presents background on Markov-reward models, as well as on the logic CSRL (syntax and semantics), before presenting an important duality result between reward and time. We discuss CSRL model-checking algorithms, and present five numerical algorithms and their computational complexity for verifying time- and reward-bounded until-properties, one of the key operators in CSRL. The versatility of our approach is illustrated through a performability case study. [ABSTRACT FROM AUTHOR]

Abstract: The “carries” when n random numbers are added base b form a Markov chain with an “amazing” transition matrix determined in a 1997 paper of Holte. This same Markov chain occurs in following the number of descents when n cards are repeatedly riffle shuffled. We give generating and symmetric function proofs and determine the rate of convergence of this Markov chain to stationarity. Similar results are given for type B shuffles. We also develop connections with Gaussian autoregressive processes and the Veronese mapping of commutative algebra. [Copyright &y& Elsevier]

Abstract  We show that a certain class of Markov chains satisfies the general Foster–Lyapunov condition under nonrestrictive assumptions. In particular, if a chain belongs to this class, the existence of an invariant measure can be established by means of the theorem provided. As an application of the theorem, the HARCH process is considered. [ABSTRACT FROM AUTHOR]

Abstract: We consider a device submitted to shocks and wear. The shocks occur with interarrival times phase-type distributed, and can induce the device failure. The device also can fail due to ageing, and the lifetime follows a phase-type distribution. The interarrival times between shocks and the lifetime depend on the number of cumulated shocks. The number of shocks that the device can support is limited. For this model, the survival probability is calculated. Other models are considered under these assumptions, and the survival functions are determined and expressed in a well-structured form. A numerical application illustrates the methods introduced in the paper. [Copyright &y& Elsevier]

Simulating electron spin resonance (ESR) spectra directly from molecular dynamics simulations of a spin-labeled protein necessitates a large number (hundreds or thousands) of relatively long (hundreds of nanoseconds) trajectories. To meet this challenge, we explore the possibility of constructing accurate stochastic models of the spin label dynamics from atomistic trajectories. A systematic, two-step procedure, based on the probabilistic framework of hidden Markov models, is developed to build a discrete-time Markov chain process that faithfully captures the internal spin label dynamics on time scales longer than about 150 ps. The constructed Markov model is used both to gain insight into the long-lived conformations of the spin label and to generate the stochastic trajectories required for the simulation of ESR spectra. The methodology is illustrated with an application to the case of a spin-labeled poly alanine α helix in explicit solvent. [ABSTRACT FROM AUTHOR]

We study information rates of time-varying flat-fading channels (FFC) modeled as finite-state Markov channels (FSMC). FSMCs have two main applications for FFCs: modeling channel error bursts and decoding at the receiver. Our main finding in the first application is that receiver observation noise can more adversely affect higher-order FSMCs than lower-order FSMCs, resulting in lower capacities. This is despite the fact that the underlying higher-order FFC and its corresponding FSMC are more predictable. Numerical analysis shows that at low to medium SNR conditions (SNR ≲ 12 dB) and at medium to fast normalized fading rates (0.01 ≲ fDT ≲ 0.10), FSMC information rates are non-increasing functions of memory order. We conclude that BERS obtained by low-order FSMC modeling can provide optimistic results. To explain the capacity behavior, we present a methodology that enables analytical comparison of FSMC capacities with different memory orders. We establish sufficient conditions that predict higher/lower capacity of a reduced-order FSMC, compared to its original high-order FSMC counterpart. Finally, we investigate the achievable information rates in FSMC-based receivers for FFCs. We observe that high-order FSMC modeling at the receiver side results in a negligible information rate increase for normalized fading rates fDT ≲ 0.01. [ABSTRACT FROM AUTHOR]

A call admission control scheme named thinning scheme, which smoothly throttles the admission rates of calls according to their priorities and aims to provide multiple prioritized traffic with a desired quality of service, is investigated under more general conditions. Using the theory of multidimensional Markov birth-death process, analytical formulas for call blocking probabilities are derived. [ABSTRACT FROM AUTHOR]

In this paper we obtain skew-product representations of the multidimensional Dunkl processes which generalize the skew-product decomposition in dimension 1 obtained in L. Gallardo and M. Yor. Some remarkable properties of the Dunkl martin-gales. Séminaire de Probabilités XXXIX, 2006. We also study the radial part of the Dunkl process, i.e. the projection of the Dunkl process on a Weyl chamber. [ABSTRACT FROM AUTHOR]

Abstract: Verification of reachability properties for probabilistic systems is usually based on variants of Markov processes. Current methods assume an exact model of the dynamic behavior and are not suitable for realistic systems that operate in the presence of uncertainty and variability. This research note extends existing methods for Bounded-parameter Markov Decision Processes (BMDPs) to solve the reachability problem. BMDPs are a generalization of MDPs that allows modeling uncertainty. Our results show that interval value iteration converges in the case of an undiscounted reward criterion that is required to formulate the problems of maximizing the probability of reaching a set of desirable states or minimizing the probability of reaching an unsafe set. Analysis of the computational complexity is also presented. [Copyright &y& Elsevier]

This article presents an overview of quantitative methodologies for the study of stage-sequential development based on extensions of Markov chain modeling. Four methods are presented that exemplify the flexibility of this approach: the manifest Markov model, the latent Markov model, latent transition analysis, and the mixture latent Markov model. A special case of the mixture latent Markov model, the so-called mover-stayer model, is used in this study. Unconditional and conditional models are estimated for the manifest Markov model and the latent Markov model, where the conditional models include a measure of poverty status. Issues of model specification, estimation, and testing using the Mplus software environment are briefly discussed, and the Mplus input syntax is provided. The author applies these 4 methods to a single example of stage-sequential development in reading competency in the early school years, using data from the Early Childhood Longitudinal Study-Kindergarten Cohort. [ABSTRACT FROM AUTHOR]

A number of authors have recently suggested solving quasi birth-and-death (QBD) processes through the use of eigenvalue-based methods. These methods take on a special form when there are multiple eigenvalues present. We investigate this problem in a general setting as well as in the context of a specific preemptive priority queueing model. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we study both bias optimality and strong n () discount optimality for denumerable discrete-time Markov decision processes. The rewards may have neither upper nor lower bounds. We give sufficient conditions on the system''s primitive data, and under which we prove (1) the existence of the bias optimality equation and bias optimal policies; (2) a condition equivalent to bias optimal policies; (3) average expected reward optimality and strong −1-discount optimality are equivalent; (4) bias optimality and strong 0-discount optimality are equivalent; (5) the existence of strong n () discount optimal stationary policies. Our conditions are weaker than those in the previous literature. Moreover, our results are illustrated by a controlled random walk. [Copyright &y& Elsevier]

  We derive the transient distribution and periodic family of asymptotic distributions and the transient and periodic moments for the quasi-birth-and-death processes with time-varying periodic rates. The distributions and moments are given in terms of integral equations involving the related random-walk process. The method is a straight-forward application of generating functions. [ABSTRACT FROM AUTHOR]

This note is concerned with constructing time-homogeneous Markov chains on a countable state-space, including an absorbing state, such that the chain has a prescribed quasi-stationary distribution. The problem is characterized in terms of the underlying Q-matrix of the process. With no restriction on the Markov chain, it is straightforward to obtain a solution. For restricted processes this is no longer the case. We look in detail at population processes of birth-death and birth-catastrophe type, and in both cases obtain explicit constructions for Markov chains with any specified quasi-stationary distribution. The results are illustrated with examples. [ABSTRACT FROM AUTHOR]

Queueing systems managed by ticket technology are widely used in service industries as well as government offices. Upon arriving at a ticket queue, each customer is issued a numbered ticket. The number currently being served is displayed. An arriving customer balks if the difference between his ticket number and the displayed number exceeds his patience level. We propose a Markov chain model of a ticket queue and develop effective evaluation tools. These tools can help management quantify the service level and identify the performance gap between the ticket queue and the conventional physical queue, in which a waiting line is formed. We gain insights about the ways customer service is affected by information loss in the ticket queue. In particular, we show that ticket and physical queues have significantly different balking probabilities when customer patience is low and the system traffic is heavy. We also propose an improvement to the ticket queue that provides each customer with his expected waiting time conditioned on his observed number difference, which is shown to raise the performance of the ticket queue to that of the physical queue. [ABSTRACT FROM AUTHOR]

We study the genealogy of so-called immortal branching processes, i.e. branching processes where each individual upon death is replaced by at least one new individual, and conclude that their marginal distributions are compound geometric. The result also implies that the limiting distributions of properly scaled supercritical branching processes are compound geometric. We exemplify our results with an expression for the marginal distribution for a class of branching processes that have recently appeared in the theory of coalescent processes and continuous stable random trees. The limiting distribution can be expressed in terms of the Fox H-function, and in special cases by the Meijer G-function. [ABSTRACT FROM AUTHOR]

In this paper we introduce the concepts of instantaneous reversibility and instantaneous entropy production rate for inhomogeneous Markov chains with denumerable state spaces. The following statements are proved to be equivalent: the inhomogeneous Markov chain is instantaneously reversible; it is in detailed balance; its entropy production rate vanishes. In particular, for a time-periodic birth-death chain, which can be regarded as a simple version of a physical model (Brownian motors), we prove that its rotation number is 0 when it is instantaneously reversible or periodically reversible. Hence, in our model of Markov chains, the directed transport phenomenon of Brownian motors can occur only in nonequilibrium and irreversible systems. [ABSTRACT FROM AUTHOR]

An artificial absorbing boundary is introduced in a linear birth and death stochastic process in order to understand the long time behavior of an ecological community. The solution is obtained by means of a spectral resolution of the probability distribution. A more general linear process with a coefficient of arbitrary strength near the boundary both with absorbing and with reflecting boundary conditions is also studied. [ABSTRACT FROM AUTHOR]

We consider the class of level-independent quasi-birth-and-death (QBD) processes that have countably many phases and generator matrices with tridiagonal blocks that are themselves tridiagonal and phase independent. We derive simple conditions for possible decay rates of the stationary distribution of the ‘level’ process. It may be possible to obtain decay rates satisfying these conditions by varying only the transition structure at level 0. Our results generalize those of Kroese, Scheinhardt, and Taylor, who studied in detail a particular example, the tandem Jackson network, from the class of QBD processes studied here. The conditions derived here are applied to three practical examples. [ABSTRACT FROM AUTHOR]

This paper gives characterizations for diffusion processes on the line and birth-death processes whose generators admit the empty essential spectra. Some equivalent conditions for empty essential spectra for general Markov generators are also discussed. [ABSTRACT FROM AUTHOR]

Abstract: Aim of this paper is to assess the fate of metapopulations described by spatially explicit models. To this end, we first present an interacting particle system (IPS) where individuals of a single species compete logistically at the local scale and can move among patches according to various dispersal kernels. As the IPS is a complex stochastic system, it is impossible to determine the persistence–extinction boundaries in any relevant parameter space with analytical methods or numerical continuation techniques. We thus resort to a heuristic method that lets us determine the boundaries as space–time percolation thresholds with a relatively modest computational effort. Such boundaries are qualitatively consistent with those we obtained with spatial implicit modelling. In particular, we find that the intermediate dispersal principle, namely that globally persistent metapopulations correspond to dispersal rates that are neither too low nor too high, turns out to be very robust even in this explicit context. However, the quantification of the boundaries strongly depends upon the number of patches, the dispersal kernels and the border conditions. Finally, we show that there exists a scaling law that relates the number of species lost in a fragmented landscape to the number of patches. Thus, the law allows a rough estimation of the cost of destroying a patch. [Copyright &y& Elsevier]

The generalized birth-death processes were introduced to model ageing of objects of different nature. The results obtained were compared with the model based on the conventional birth-death processes. [ABSTRACT FROM AUTHOR]

This paper discusses multiserver feedback retrial queues with balking and control retrial rate. This system is analyzed as a quasi-birth-and-death (QBD) process and the necessary and sufficient condition for stability of the system is discussed. Some interesting system performance measures are obtained using matrix geometric method. The effects of various parameters on the system performance measures are illustrated numerically. Finally, the optimization of the retrial rate and specific probabilistic descriptors of the system are investigated. [ABSTRACT FROM AUTHOR]

In this study, we characterize the equilibrium behavior of spatial migration processes that represent population migrations, or birth-death processes, in general spaces. These processes are reversible Markov jump processes on measure spaces. As a precursor, we present fundamental properties of reversible Markov jump processes on general spaces. A major result is a canonical formula for the stationary distribution of a reversible process. This involves the characterization of two-way communication in transitions, using certain Radon-Nikodým derivatives. Other results concern a Kolmogorov criterion for reversibility, time reversibility, and several methods of constructing or identifying reversible processes. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we combine 3D anisotropic diffusion and motion estimation for image denoising and improvement of motion estimation. We compare different continuous isotropic nonlinear and anisotropic diffusion processes, which can be found in literature, with a process especially designed for image sequence denoising for motion estimation. All of these processes initially improve motion estimation due to reduction of noise and high frequencies. But while all the well known processes rapidly destroy or hallucinate motion information, the process brought forward here shows considerably less information loss or violation even at motion boundaries. We show the superior behavior of this process. Further we compare the performance of a standard finite difference diffusion scheme with several schemes using derivative filters optimized for rotation invariance. Using the discrete scheme with least smoothing artifacts we demonstrate the denoising capabilities of this approach. We exploit the motion estimation to derive an automatic stopping criterion. [Copyright &y& Elsevier]

Recently, risk processes have been analyzed as fluid queues. That approach is adapted here to the analysis of the token bucket model for Markovian traffic patterns. This paper presents the Laplace transform of the time until a given traffic pattern is not compliant anymore with a particular token bucket model. [ABSTRACT FROM AUTHOR]

The purpose of this article is to present analytic methods for determining the asymptotic behaviour of the coefficents of power series that can be applied to homogeneous discrete quasi death and birth processes. It turns that there are in principle only three types for the asymptotic behaviour. The process either converges to the stationary distribution or it can be approximated in terms of a reflected Brownian motion or by a Brownian motion. In terms of Markov chains these cases correspond to positive recurrence, to null recurrence, and to non recurrence. The same results hold for the continuous case, too. [ABSTRACT FROM AUTHOR]

In this paper, we consider a retrial queueing system consisting of a waiting line of infinite capacity in front of a single server subject to breakdowns. A customer upon arrival may join the queue (waiting line) or go to the retrial orbit (another queue) to retry for service after a random time. Only the customer at the head of the retrial orbit is allowed to retry for service. Upon retrial, the customer enters the service if the server is idle; otherwise, it may go back to the retrial orbit or leave the system (become impatient). All the interarrival times, service times, server up times, server down times and retrial times are exponential, and all the necessary independence conditions in these variables are assumed. For this system, we provide sufficient conditions under which, for any given number of customers in the orbit, the stationary probability of the number of customers in the waiting line decays geometrically. We also provide explicitly an expression for the decay parameter. [ABSTRACT FROM AUTHOR]