Taking up a recent proposal by Stadje and Parthasarathy in the setting of the many-server Poisson queue, we consider the integral ∫∞ 0 [limu→∞E(X(u))− E(X(t))]dt as a measure of the speed of convergence towards stationarity of the process {X(t), t ≥ 0}, and evaluate the integral explicitly in terms of the parameters of the process in the case that {X(t), t ≥ 0} is an ergodic birth-death process...

This note presents a method of evaluating the distribution of a path integral for Markov chains on a countable state space. We illustrate the method with reference to several models, including birth-death processes and the birth, death and catastrophe process.

The convergence of the transient mean of a nite birth and death process (BDP) to its stationary value is studied. Closed-form solutions are obtained for speciic nite BDPs. This contrasts with the computational diiculties encountered in solving numerically the BDPs with general birth and death rates.

Under the in ̄uence of randomly occurring disasters, the eventual extinction probability, q, of a birth and death process, Z, is a random variable. In this paper, we obtain an integral expression for the probability density function g…x† of q under the assumption that the population process Z is a time homogeneous linear birth and death process and the disasters occur according to an arbitrary r...

Abstract. The ancestral selection graph in population genetics introduced by Krone and Neuhauser (1997) is an analogue to the coalescent genealogy. The number of ancestral particles, backward in time, of a sample of genes is an ancestral process, which is a birth and death process with quadratic death and linear birth rate. In this paper an explicit form of the number of ancestral particle is o...

consider the random walk among n places with n(n - 1)/2 transports. we attach an exponential random variable xij to each transport between places pi and pj and take these random variables mutually independent. if transports are possible or impossible independently with probability p and 1-p, respectively, then we give a lower bound for the distribution function of the smallest path at point log...

objective: childbirth is one of the most vulnerable moments and the most important and memorable events in the lives of women that despite of bringing happiness, it can be associated with psychological trauma and endanger the mother and neonate health. mothers' perception of the psychological birth trauma is a highly subjective process that depends on the cultural, social and biological conditi...

Birth-death processes have been widely used for different biological applications, the most common of which is stochastic modeling of population dynamics. A review of these applications can be found in Novozhilov et al. (2006). In this letter we illustrate a method to obtain approximate formulae for the steady-state mean and variance, of a birth death process involving a single species with arb...

Evolutionary models on graphs, as an extension of the Moran process, have two major implementations: birth-death (BD) models (or the invasion process) and death-birth (DB) models (or voter models). The isothermal theorem states that the fixation probability of mutants in a large group of graph structures (known as isothermal graphs, which include regular graphs) coincides with that for the mixe...

A birth and death process is considered in which X,(t) is the number of open channels in a patch of membrane containing n channels. The voltage response of such a patch to conductance fluctuations is obtained including moments and spectral density. Furthermore, a diffusion approximation, an Ornstein-Uhlenbeck process, is obtained based on a weak convergence result to represent the patch conduct...