Stationarity and quasi-stationarity for birth-death processes
نویسندگان
چکیده
منابع مشابه
Large Deviations and Quasi-stationarity for Density-dependent Birth-death Processes
Consider a density-dependent birth-death process X N on a finite state space of size N . Let PN be the law (on D.[0; T ]/ where T > 0 is arbitrary) of the density process XN =N and let 5N be the unique stationary distribution (on [0,1]) of X N =N , if it exists. Typically, these distributions converge weakly to a degenerate distribution as N ! 1, so the probability of sets not containing the de...
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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...
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In this paper we give some general, but easy-to-check, conditions guaranteeing the quasistationarity and quasi-ergodicity of Markov processes. We also present several classes of Markov processes satisfying our conditions. AMS 2010 Mathematics Subject Classification: Primary 60F25, 60J25G20; Secondary 60J35, 60J75
متن کاملOn the Convergence to Stationarity of Some Finite Birth and Death Processes
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.
متن کاملQuasi - 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...
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ژورنال
عنوان ژورنال: SCIENTIA SINICA Mathematica
سال: 2019
ISSN: 1674-7216
DOI: 10.1360/n012018-00047