Stability of Markovian processes III: Foster–Lyapunov criteria for continuous-time processes

Advances in Applied Probability - Tập 25 Số 3 - Trang 518-548 - 1993
Sean Meyn1, Richard L. Tweedie2
1University of Illinois

Tóm tắt

In Part I we developed stability concepts for discrete chains, together with Foster–Lyapunov criteria for them to hold. Part II was devoted to developing related stability concepts for continuous-time processes. In this paper we develop criteria for these forms of stability for continuous-parameter Markovian processes on general state spaces, based on Foster-Lyapunov inequalities for the extended generator.Such test function criteria are found for non-explosivity, non-evanescence, Harris recurrence, and positive Harris recurrence. These results are proved by systematic application of Dynkin's formula.We also strengthen known ergodic theorems, and especially exponential ergodic results, for continuous-time processes. In particular we are able to show that the test function approach provides a criterion forf-norm convergence, and bounding constants for such convergence in the exponential ergodic case.We apply the criteria to several specific processes, including linear stochastic systems under non-linear feedback, work-modulated queues, general release storage processes and risk processes.

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Advances in Applied Probability

Tập 25 Số 3

518-548

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