Survival in a quasi-death process

Survival in a quasi-death process

We consider a Markov chain in continuous time with one absorbing state and a finite set S of transient states. When S is irreducible the limiting distribution of the chain as t → ∞, conditional on survival up to time t, is known to equal the (unique) quasi-stationary distribution of the chain. We address the problem of generalizing this result to a setting in which S may be reducible, and show ...

Stationary Distribution of a Perturbed Quasi-birth-and-death Process

Quasi-Birth-and-Death Processes with Rational Arrival Process Components

In this paper we introduce the concept of a Quasi-Birth-and-Death process (QBD) with Rational Arrival Process components. We use the physical interpretation of a Rational Arrival Process (RAP), developed by Asmussen and Bladt, to consider such a Markov process. We exploit this interpretation to develop an analytic method for such a process, that parallels the analysis of a traditional QBD. We d...

Quasi - Birth - Death Processes

1 Description of the Model This case study is analog to the one described in [2]. We considered a system consisting of a fixed number of m processors and an infinite queue for storing job requests. The processing speed of a processor is described by the rate γ, while λ describes the incoming rate of new jobs. If a new job arrives while at least one processor is idle, the job will be processed d...

Minimal quasi-stationary distribution approximation for a birth and death process

In a first part, we prove a Lyapunov-type criterion for the ξ1-positive recurrence of absorbed birth and death processes and provide new results on the domain of attraction of the minimal quasi-stationary distribution. In a second part, we study the ergodicity and the convergence of a Fleming-Viot type particle system whose particles evolve independently as a birth and death process and jump on...