On a maximum of nearest-neighbor random walk with asymptotically zero drift on lattice of positive half line

2020/04/26 by Hongyan Sun, Huaming Wang, Sun, Hongyan +1 · 1 citation
Decision Sciences · Mathematics · Computer Science · #Probability and Risk Models #Stochastic processes and statistical mechanics #Bayesian Methods and Mixture Models

paper · pdf · doi:10.48550/arxiv.2004.12422

Abstract

Consider a nearest-neighbor random walk with certain asymptotically zero drift on the positive half line. Let M be the maximum of an excursion starting from 1 and ending at 0. We study the distribution of M and characterize its asymptotics, which is quite different from those of simple random walks.

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