Related papers: Approximation of the birth process
We consider the almost semi-continuous processes defined on a finite Markov chain. The representation of the moment generating functions for the absolute maximum after achievement positive level and for the recovery time are obtained.…
Obtaining estimates of the convergence rate of the regenerating process $Q(t)$ whose value at time $t$ is equal to the number of claims in the system $ M \backslash G \backslash \infty $ at this moment, to the limit (stationary) regime.
In this note, a general approach to the study of non-stationary Markov chains with catastrophes and the corresponding queuing models is considered, as well as to obtain estimates of the limiting regime itself. As an illustration, an example…
Data on count processes arise in a variety of applications, including longitudinal, spatial and imaging studies measuring count responses. The literature on statistical models for dependent count data is dominated by models built from…
A single queueing system with time-dependent exponentially distributed arrival processes and exponential machine processes (Kendall notation $M_t/M_t/1$) is analyzed. Modeling the time evolution for the discrete queue-length distribution by…
This paper studies the sensitivity analysis of mass-action systems against their diffusion approximations, particularly the dependence on population sizes. As a continuous time Markov chain, a mass-action system can be described by a…
Potential theory is a central tool to understand and analyse Markov processes. In this article, we develop its probabilistic counterpart for branching Markov chains. Specifically, we examine versions of quasi-processes or interlacements…
The paper deals with a certain class of random evolutions. We develop a construction that yields an invariant measure for a continuous-time Markov process with random transitions. The approach is based on a particular way of constructing…
A multi-channel queueing system is considered. The arriving requests differ in their type. Requests of each type arrive according to a Poisson process. The number of channels required for service with the rate equal to 1 depends of the…
Convergence of stochastic processes with jumps to diffusion processes is investigated in the case when the limit process has discontinuous coefficients. An example is given in which the diffusion approximation of a queueing model yields a…
We are concerned with the absolute continuity of stationary distributions corresponding to some piecewise deterministic Markov process, being typically encountered in biological models. The process under investigation involves a…
This note is motivated by connections between the online and offline problems of selecting a possibly long subsequence from a Poisson-paced sequence of uniform marks under either a monotonicity or a sum constraint. The offline problem with…
This study explores a Gaussian quasi-likelihood approach for estimating parameters of diffusion processes with Markovian regime switching. Assuming the ergodicity under high-frequency sampling, we will show the asymptotic normality of the…
This paper is concerned with the development of rigorous approximations to various expectations associated with Markov chains and processes having non-stationary transition probabilities. Such non-stationary models arise naturally in…
We study ergodic properties of a class of Markov-modulated general birth-death processes under fast regime switching. The first set of results concerns the ergodic properties of the properly scaled joint Markov process with a parameter that…
Queueing networks are systems of theoretical interest that find widespread use in the performance evaluation of interconnected resources. In comparison to counterpart models in genetics or mathematical biology, the stochastic (jump)…
We study the Patient Assignment Scheduling (PAS) problem in a random environment that arises in the management of patient flow in the hospital systems, due to the stochastic nature of the arrivals as well as the Length of Stay distribution.…
We consider Poisson's equation for quasi-birth-and-death processes (QBDs) and we exploit the special transition structure of QBDs to obtain its solutions in two different forms. One is based on a decomposition through first passage times to…
We consider a general method for the approximation of the distribution of a process conditioned to not hit a given set. Existing methods are based on particle system that are failable, in the sense that, in many situations , they are not…
We present a perfect simulation algorithm for measures that are absolutely continuous with respect to some Poisson process and can be obtained as invariant measures of birth-and-death processes. Examples include area- and…