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Determines the conditions on the birth and death rates of a birth-death process for the process to be a member of a family of similar processes. Families of similar birth-death processes; Birth-death processes with finite state space.

Examines the application of the perfect simulation Coupling from the Past method to locally stable point processes. Equilibrium distributions of spatial birth-and-death processes; Accounts of the discrete-time Metropolis-Hastings samplers for point processes; Incorporation of perfect simulation into Strauss point process.

Examines the relationship between birth-and-death processes, lattice path combinatorics and continued fractions. Creation of a correspondence between birth-and-death processes and Stieltjes-Jacobi continued fraction; Correlation of weighted lattice paths to continued fractions; Accounts of obtaining Laplace transforms of transient characteristics.

The analysis of finite-buffered, unreliable production lines is often based on the method of decomposition, where the original system is decomposed into a series of two-stage subsystems that can be modeled as quasi birth-death processes. In this paper, we present methods for computing the gradients of the equilibrium distribution vector for such processes. Then we consider a specific production line with finite buffers and machine breakdowns and develop an algorithm that incorporates gradient estimation into the framework of Gershwin's approximate decomposition. The algorithm is applied to the problem of workforce allocation to the machines of a production line to maximize throughput. It is shown that this problem is equivalent to a convex mathematical programming problem and, therefore, a globally optimal solution can be obtained. [ABSTRACT FROM AUTHOR]

An approach making it possible to obtain estimates of certain probabilities related to inhomogeneous multidimensional birth-and-death processes is proposed. [ABSTRACT FROM AUTHOR]

Presents information on a study which investigated the Laplace theory. Transient characteristics associated with the birth and death processes; Methodology of the study; Discussion on the results; Conclusion.

Provides a probabilistic proof of the Stein's factors based on Markov birth and death Markov chains. Why the Stein's factors are important in applying the Stein-Chem method in Poisson approximation; Estimation of the Stein's factors.

Discusses the standard bivariate death process and other Markovian modification and extensions that are of interest in the field of epidemic modeling. Development of an approach that permits the derivation of the exact distribution of the population state at any point in time; Derivation of a central system of relations with two indices for the temporal state distribution.

Presents information on a study which focused on a quality-based birth-and-death queueing model used for evaluating the performance of a code-division multiple access cellular mobile communication system. Performance analysis via quality-based birth-death queueing model; Numerical examples and discussions.

We consider the problem of optimally meeting a stochastically growing demand for capacity over an infinite horizon. Under the assumption that demand for product follows either a nonlinear Brownian motion or a non-Markovian birth and death process, we show that this stochastic problem can be transformed into an equivalent deterministic problem. Consistent with earlier work by A. Manne, the equivalent problem is formed by replacing the stochastic demand by its deterministic trend and discounting all costs by a new interest rate that is smaller than the original, in approximate proportion to the uncertainty in the demand. [ABSTRACT FROM AUTHOR]

We start with a stochastic flow of diffeomorphisms of the space. Particles enter the space at random times and places. Each particle is carried by the flow for some random amount of time. We examine the point process formed by the particles at a fixed time, on the evolution of that point process as time varies, and on the equilibrium law of the point process. [ABSTRACT FROM AUTHOR]

Describes a spatial symmetry for first-passage-time (FPT) problem for birth-and-death (BD) processes. Details on BD processes; Analysis of truncated BD processes; Symmetry properties for truncated BD processes.

Discusses regularity and reversibility for birth-death-migration processes. Application of Markov chains; Conditions for recurrence; Correlation of geographic distribution and dynamics of population growth.

The variance of a time average is important for planning, running and interpreting experiments. This paper derives a simple method to find this variance for the case of a Markov process. This method is then applied to obtain the variance of a time average for the case of a birth-death process. [ABSTRACT FROM AUTHOR]

This paper presents an iterative, seminumerical method for solving the balance equations of finite two-dimensional birth and death processes The method is seminumerical in that it uses the formal knowledge of the stationary probability distribution of one variable, and the iteration is applied to the conditional probabilities of the second variable given the first one. Sufficient convergence conditions for this approach are discussed. An always convergent entirely numerical alternative solution is also presented. Empirical results indicate that both methods perform, in many cases, several times better (in terms of time required) than the commonly used Gauss-Seidel method. Possible generalizations to processes of more than two dimensions are also indicated. [ABSTRACT FROM AUTHOR]

We construct a model of economic growth in which firms adopt more advanced technologies. In order to advance its technology, a firm must make an investment. The size of this investment depends on the size of the technology adoption barriers in the firm's country Assuming a Markov chain for these barriers, we examine the amount of variation and persistence in the chain for which the model matches the observed output disparity across countries and the mobility of nations. Our calibration suggests a range for the size of these barriers of a factor five, and the presence of a barrier trap. [ABSTRACT FROM AUTHOR]

Green, Kolesar and Svoronos (in press) and Green and Kolesar (in press) use numerical methods to investigate the behavior of multiserver Markov queues with a Poisson arrival process having a sinusoidal arrival rate. For this model they propose an approximation for long-run average performance measures called the pointwise stationary approximation (PSA), which consists of an appropriate weighted average of the performance measure that would result at each point in time if the system were stationary with the arrival rate that applies at that point in time. In this paper we verify their conjecture that PSA is asymptotically correct as the service and arrival rates increase with the instantaneous traffic intensity held fixed (corresponding to long arrival rate cycles). We actually establish both pointwise and average versions of this result for general time-dependent birth-and-death processes. [ABSTRACT FROM AUTHOR]

We consider either a discrete time or an age-dependent branching process where the population consists of k types of individuals Each time an individual is born, an action is chosen for him which affects his lifetime, the number and types of his offspring, and the reward received. The problem of maximizing the expected reward is shown to be equivalent to a generalized Markov decision problem where the (k x k) transition matrices are non-negative but not necessarily substochastic. It is shown that this branching process decision model can account for immigration, that it can be viewed as a controlled population process or infinite particle system, and that it has a number of applications including marketing and biology. [ABSTRACT FROM AUTHOR]

Motivated by a planning horizon result for continuous time Markov decision chains, we study decision rules, called preferred, which may be used in the initially stationary part of nearly optimal policies. We characterize these rules and then, under conditions involving state recurrence and accessibility, consider finding such rules. We also discuss the connection between preferred rules and certain discounted process decision rules, and the role of preferred rules in optimal policies. [ABSTRACT FROM AUTHOR]

This article discusses a model for the lineage of a growing population as an age-dependent branching process. Branching processes are mathematical representations of the development of populations whose members reproduce and die according to the rules of chance. Applications of branching processes can be found in a wide variety of disciplines. The simplest type of biological population growth to which age-dependent branching processes can be applied is when reproduction occurs only once during the life of the organism. Age-dependent birth and death processes can also be extended to the case where organisms reproduce more than once in their lifetime.

Analyzes limiting conditional distributions for birth-death processes. Quasi-stationary distributions for a non-explosive; Evanescent processes; Certainty of absorption; Transition rates; Kolmogorov differential equations.

This paper presents results for queueing systems that are characterized by poisson arrival epochs with χ (a random variable) arrivals at each epoch, exponential service times and c servers. The steady state probabilities, the probability of blocking (not being served immediately) for both loss and delay systems are investigated. In addition, the average delay, the variance of the delay and the delay distribution for first-come-served by batches and arbitrary order of service within batches are presented. [ABSTRACT FROM AUTHOR]

A large sample theory for birth and death queuing processes which are ergodic and metrically transitive is applied to make inferences about arrival and service rates. Likelihood ratio tests and maximum likelihood estimators are derived for simple models. Composite hypotheses, for example that the arrival rate does not vary with the number in the system, are considered. A numerical example illustrating these results, based on data generated by simulating a known model, is presented, which includes the testing of both true and false composite hypotheses. [ABSTRACT FROM AUTHOR]

The article discusses research on the relationship between the social networks of primates and the promotion of cooperation. The study utilized a death-birth (DB) update rule mechanism in the simulation of the evolution of a cooperative behaviour in 70 primate groups. The community modularity of primate groups was calculated in order to quantify their heterogeneity. The study found that network reciprocity increased the fixation probability for cooperation for most groups.

A letter to the editor is presented which offers mathematical information on birth and death processes (BDPs).

Using the continuous-time susceptible-infected-susceptible (SIS) model on networks, we investigate the problem of inferring the class of the underlying network when epidemic data is only available at population-level (i.e., the number of infected individuals at a finite set of discrete times of a single realisation of the epidemic), the only information likely to be available in real world settings. To tackle this, epidemics on networks are approximated by a Birth-and-Death process which keeps track of the number of infected nodes at population level. The rates of this surrogate model encode both the structure of the underlying network and disease dynamics. We use extensive simulations over Regular, Erdős–Rényi and Barabási–Albert networks to build network class-specific priors for these rates. We then use Bayesian model selection to recover the most likely underlying network class, based only on a single realisation of the epidemic. We show that the proposed methodology yields good results on both synthetic and real-world networks. [ABSTRACT FROM AUTHOR]

Regretably, there are a number of significant errors in Moschopoulos and Shpak, (2010).Communications in Statistics—Theory and Methods39:1761–1775. Most are typographic errors that have the potential to cause confusion, and in some instances, have carried through to several equations. [ABSTRACT FROM PUBLISHER]

We study a Brownian particle diffusing under a time-modulated stochastic resetting mechanism to a fixed position. The rate of resetting r(t) is a function of the time t since the last reset event. We derive a sufficient condition on r(t) for a steady-state probability distribution of the position of the particle to exist. We derive the form of the steady-state distributions under some particular choices of r(t) and also consider the late time relaxation behavior of the probability distribution. We consider first passage time properties for the Brownian particle to reach the origin and derive a formula for the mean first passage time (MFPT). Finally, we study optimal properties of the MFPT and show that a threshold function is at least locally optimal for the problem of minimizing the MFPT. [ABSTRACT FROM AUTHOR]

One of the central objectives in the field of phylodynamics is the quantification of population dynamic processes using genetic sequence data or in some cases phenotypic data. Phylodynamics has been successfully applied to many different processes, such as the spread of infectious diseases, within-host evolution of a pathogen, macroevolution and even language evolution. Phylodynamic analysis requires a probability distribution on phylogenetic trees spanned by the genetic data. Because such a probability distribution is not available for many common stochastic population dynamic processes, coalescent-based approximations assuming deterministic population size changes are widely employed. Key to many population dynamic models, in particular epidemiological models, is a period of exponential population growth during the initial phase. Here, we show that the coalescent does not well approximate stochastic exponential population growth, which is typically modelled by a birth-death process. We demonstrate that introducing demographic stochasticity into the population size function of the coalescent improves the approximation for values of R0 close to 1, but substantial differences remain for large R0. In addition, the computational advantage of using an approximation over exact models vanishes when introducing such demographic stochasticity. These results highlight that we need to increase efforts to develop phylodynamic tools that correctly account for the stochasticity of population dynamic models for inference. [ABSTRACT FROM AUTHOR]

In his paper "Optimal Inventory Policies when Ordering Prices are Random" that appeared in the May-June 1985 issue of the journal "Operations Research," Kamal Golabi presents a general treatment of the random price, finite-horizon inventory problem. In this paper "Stockpiling under Price Uncertainty and Storage Capacity Constraints," which is not among Golabi's references, He treated a version of the random price inventory problem. He considered prices determined by a discrete time Markov process, and dealt with the stationary, infinite-horizon discounted problem with linear holding costs. The optimal policy derived in Magirou is also characterized in terms of critical numbers defined recursively. These results coincide with those of Golabi in the infinite horizon discounted case. When holding costs are not linear, a value-space approach becomes unwieldy, since the property of piecewise linearity does not carry over. However, the value-space approach has several advantages since it can deal successfully with Markov prices, inventory constraints and speculative behavior.

Results in another paper in this issue may raise the question of whether for finite state and action, continuous time parameter Markov decision chains there always exists an initially stationary optimal policy. We give an example in which there is no such policy. [ABSTRACT FROM AUTHOR]

Taylor's power law describes an empirical relationship between the mean and variance of population densities in field data, in which the variance varies as a power, b, of the mean. Most studies report values of b varying between 1 and 2. However, Cohen (2014a) showed recently that smooth changes in environmental conditions in a model can lead to an abrupt, infinite change in b. To understand what factors can influence the occurrence of an abrupt change in b, we used both mathematical analysis and Monte Carlo samples from a model in which populations of the same species settled on patches, and each population followed independently a stochastic linear birth-and-death process. We investigated how the power relationship responds to a smooth change of population growth rate, under different sampling strategies, initial population density, and population age. We showed analytically that, if the initial populations differ only in density, and samples are taken from all patches after the same time period following a major invasion event, Taylor's law holds with exponent b = 1, regardless of the population growth rate. If samples are taken at different times from patches that have the same initial population densities, we calculate an abrupt shift of b, as predicted by Cohen (2014a). The loss of linearity between log variance and log mean is a leading indicator of the abrupt shift. If both initial population densities and population ages vary among patches, estimates of b lie between 1 and 2, as in most empirical studies. But the value of b declines to ~1 as the system approaches a critical point. Our results can inform empirical studies that might be designed to demonstrate an abrupt shift in Taylor's law. [ABSTRACT FROM AUTHOR]

Algebraic discussions are developed to derive transition probabilities for a simple time-inhomogeneous birth–death process. Algebraic probability theory and Lie algebraic treatments make it easy to treat the time-inhomogeneous cases. As a result, an expression based on the Charlier polynomials is obtained, which can be considered as an extension of a famous Karlin–McGregor representation for a time-homogeneous birth–death process. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new probabilistic method which integrates building extraction with change detection in remotely sensed image pairs. A global optimization process attempts to find the optimal configuration of buildings, considering the observed data, prior knowledge, and interactions between the neighboring building parts. We present methodological contributions in three key issues: 1) We implement a novel object-change modeling approach based on Multitemporal Marked Point Processes, which simultaneously exploits low-level change information between the time layers and object-level building description to recognize and separate changed and unaltered buildings. 2) To answer the challenges of data heterogeneity in aerial and satellite image repositories, we construct a flexible hierarchical framework which can create various building appearance models from different elementary feature-based modules. 3) To simultaneously ensure the convergence, optimality, and computation complexity constraints raised by the increased data quantity, we adopt the quick Multiple Birth and Death optimization technique for change detection purposes, and propose a novel nonuniform stochastic object birth process which generates relevant objects with higher probability based on low-level image features. [ABSTRACT FROM AUTHOR]