Nonlinear renewal theory for Markov random walks

Vincent F. Melfi

Stochastic Processes and their Applications, 1994, vol. 54, issue 1, 71-93

Abstract: Let {Sn} be a Markov random walk satisfying the conditions of Kesten's Markov renewal theorem. It is shown that if {Zn} is a stochastic process whose finite-dimensional, conditional distributions are asymptotically close to those of {Sn} (in the sense of weak convergence), then the overshoot of {Zn} has the same limiting distribution as that of {Sn}. In the case where {Zn} can be represented as a perturbed Markov random walk, this allows substantial weakening of the slow change condition on the perturbation process; more importantly, no such representation is required. An application to machine breakdown times is given.

Keywords: Markov; random; walk; Nonlinear; renewal; theory; Prokhorov; metric; Markov; renewal; theory (search for similar items in EconPapers)
Date: 1994
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