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Hitting times for the perturbed reflecting random walk

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  • Serlet, Laurent

Abstract

We consider a nearest neighbor random walk on Z which is reflecting at 0 and perturbed when it reaches its maximum. We compute the law of the hitting times and derive many corollaries, especially invariance principles with (rather) explicit descriptions of the asymptotic laws. We also obtain some results on the almost sure asymptotic behavior. As a by-product one can derive results on the reflecting Brownian motion perturbed at its maximum.

Suggested Citation

  • Serlet, Laurent, 2013. "Hitting times for the perturbed reflecting random walk," Stochastic Processes and their Applications, Elsevier, vol. 123(1), pages 110-130.
    • Handle: RePEc:eee:spapps:v:123:y:2013:i:1:p:110-130
    DOI: 10.1016/j.spa.2012.09.003
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    References listed on IDEAS

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    1. Chaumont, L. & Doney, R. A., 2000. "Some calculations for doubly perturbed Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 85(1), pages 61-74, January.
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