Abstract
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.
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Serlet, L. (2018). Explicit Laws for the Records of the Perturbed Random Walk on \(\mathbb {Z}\) . In: Donati-Martin, C., Lejay, A., Rouault, A. (eds) Séminaire de Probabilités XLIX. Lecture Notes in Mathematics(), vol 2215. Springer, Cham. https://doi.org/10.1007/978-3-319-92420-5_14
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DOI: https://doi.org/10.1007/978-3-319-92420-5_14
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