Explicit Laws for the Records of the Perturbed Random Walk on \(\mathbb {Z}\)

  • Laurent Serlet
Part of the Lecture Notes in Mathematics book series (LNM, volume 2215)


We consider a nearest neighbor random walk on \(\mathbb {Z}\) which is perturbed when it reaches its extrema, as considered before by several authors. We give invariance principles for the signs of the records, the values of the records, the times of the records, the number of visited points, with explicit asymptotic Laplace transforms and/or densities.


Perturbed random walk Once-reinforced random walk Perturbed Brownian motion Records Invariance principle Recurrence 


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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques Blaise Pascal (CNRS UMR 6620)Université Clermont AuvergneAubièreFrance

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