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The generalized Kolmogorov criterion

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  • Pollett, P. K.

Abstract

In this paper we further develop a method, touched upon Pollett (1988), of determining quasistationary distributions for a continuous-time Markov chain directly from the matrix of transition rates, Q. In particular, we establish criteria for determining whether or not a given q-matrix, Q' is a [mu]-reverse or [mu]-dual of Q. A detail-balance relationship between Q' and Q then provides a straightforward means for determining [mu]-invariant measures and vectors for Q, and hence facilitates the evaluation of quasistationary distributions. We illustrate our results by considering the birth, death and catastrophe process and some examples of random walks.

Suggested Citation

  • Pollett, P. K., 1989. "The generalized Kolmogorov criterion," Stochastic Processes and their Applications, Elsevier, vol. 33(1), pages 29-44, October.
    • Handle: RePEc:eee:spapps:v:33:y:1989:i:1:p:29-44
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