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Nonlinear renewal theory for Markov random walks

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  • Melfi, Vincent F.

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.

Suggested Citation

  • Melfi, Vincent F., 1994. "Nonlinear renewal theory for Markov random walks," Stochastic Processes and their Applications, Elsevier, vol. 54(1), pages 71-93, November.
    • Handle: RePEc:eee:spapps:v:54:y:1994:i:1:p:71-93
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