New Methods for Determining Quasistationary Distributions for Markov Chains
نویسنده
چکیده
We shall be concerned with the problem of determining quasista-tionary distributions for Markovian models directly from their transition rates Q. We shall present simple conditions for a-invariant measure m for Q to be-invariant for the transition function, so that if m is nite it can be normalized to produce a quasistationary distribution.
منابع مشابه
Direct analytical methods for determining quasistationary distributions for continuous-time Markov chains
We shall be concerned with the problem of determining the quasistationary distributions of an absorbing continuous-time Markov chain directly from the transition-rate matrix Q. We shall present conditions which ensure that any finite μ-invariant probability measure for Q is a quasistationary distribution. Our results will be illustrated with reference to birth and death processes. QUASISTATIONA...
متن کاملQuasistationary Distributions for Continuous-Time Markov Chains
Quasistationary Distributions for Continuous-Time Markov Chains – p.1
متن کاملApproximations of Quasistationary Distributions for Markov Chains
We consider a simple and widely used method for evaluating quasistationary distributions of continuous time Markov chains. The infinite state space is replaced by a large, but finite approximation, which is used to evaluate a candidate distribution. We give some conditions under which the method works, and describe some important pitfalls. μ-subinvariant measures; conditioned processes; limitin...
متن کاملQuasistationary Distributions for Continuous Timemarkov Chains
Recently, Elmes, Pollett and Walker 2] proposed a deenition of a quasistationary distribution to accommodate absorbing Markov chains for which absorption occurs with probability less than 1. We will show that the probabilistic interpretation pertaining to cases where absorption is certain (van Doorn 13]) does not hold in the present context. We prove that the state probabilities at time t condi...
متن کاملFurther Results on the Relationship between -invariant Measures and Quasistationary Distributions for Absorbing Continuous-time Markov Chains
This note considers continuous-time Markov chains whose state space consists of an irreducible class, C, and an absorbing state which is accessible from C. The purpose is to provide results on-invariant and-subinvariant measures where absorption occurs with probability less than 1. In particular, the well known premise that the-invariant measure, m, for the transition rates be nite is replaced ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007