Stationary Distribution of a Perturbed Quasi-birth-and-death Process
نویسندگان
چکیده
منابع مشابه
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...
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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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For Markov processes on the positive integers with the origin as an absorbing state, Ferrari, Kesten, Martinez and Picco [4] studied the existence of quasi-stationary and limiting conditional distributions by characterizing quasi-stationary distributions as fixed points of a transformation Φ on the space of probability distributions on {1, 2, . . .}. In the case of a birth-death process, one ca...
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This paper is concerned with the circumstances under which a discrete-time absorbing Markov chain has a quasi-stationary distribution. We showed in a previous paper that a pure birth-death process with an absorbing bottom state has a quasi-stationary distribution – actually an infinite family of quasi-stationary distributions – if and only if absorption is certain and the chain is geometrically...
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The Karlin-McGregor representation for the transition probabilities of a birth-death process with an absorbing bottom state involves a sequence of orthogonal polynomials and the corresponding measure. This representation can be generalized to a setting in which a transition to the absorbing state (killing) is possible from any state rather than just one state. The purpose of this paper is to in...
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تاریخ انتشار 2012