Hitting times for the perturbed reflecting random walk

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 in-variance principles with (rather) explicit descriptions of the asymptotic laws. We obtain also 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.
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Laurent Serlet. Hitting times for the perturbed reflecting random walk. Stochastic Processes and their Applications, Elsevier, 2013, 123 (1), pp.110-130. ⟨10.1016/j.spa.2012.09.003⟩. ⟨hal-02419818⟩

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