Abstract: In this paper we study a transient birth and death Markov process penalized by its sojourn time in 0. Under the new probability measure the original process behaves as a recurrent birth and death Markov process. We also show, in a particular case, that an initially recurrent birth and death process, behaves as an transient birth and death process after penalization with the event that...

In this paper we study the long term evolution of a continuous time Markov chain formed by two interacting birth-and-death processes and motivated by modelling interaction between populations. We show transience/recurrence of the Markov chain under fairly general assumptions on transition rates and describe in more detail its asymptotic behaviour in some transient cases. 1 The model and results...

We are interested in describing the infected size of SIS Epidemic model using Birth-Death Markov process. The Susceptible-Infected-Susceptible (SIS) is defined within a population constant $M$; kept by replacing each death with newborn healthy individual. life span individual modelled an exponential distribution parameter $\alpha$; and disease spreads Poisson process rate $\lambda_{I}$. $\lambd...

Aiming at reduction of complexity, this work is concerned with two-time-scale Markov chains and applications to quasi-birth-death queues. Asymptotic expansions of probability vectors are constructed and justified. Lumping all states of the Markov chain in each subspace into a single state, an aggregated process is shown to converge to a continuous-time Markov chain whose generator is an average...

A general integral for birth±death Markov processes is considered. A closed form expression is provided for its expected value in terms of the birth and death rates. A simple route for numerical evaluation of its variance is also suggested. Ó 2000 Elsevier Science Inc. All rights reserved. Keywords: Birth±death process; Hitting time; Integral of Markov process Hern andez-Su arez and Castillo-Ch...

In this paper algorithms for model checking CSL (continuous stochastic logic) against infinite-state continuous-time Markov chains of so-called quasi birth-death type are developed. In doing so we extend the applicability of CSL model checking beyond the recently proposed case for finite-state continuous-time Markov chains, to an important class of infinite-state Markov chains. We present synta...

This paper deals with the Markov modeling and reliability analysis of urea synthesis system of a fertilizer plant. This system was modeled using Markov birth–death process with the assumption that the failure and repair rates of each subsystem follow exponential distribution. The first-order Chapman–Kolmogorov differential equations are developed with the use of mnemonic rule and these equation...