Hongyan Sun, Hua-Ming Wang
Published 2020-04-26Version 1
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.
Asymptotics of product of nonnegative 2-by-2 matrices and maximum of a (2,1) random walk with asymptotically zero drift
Angular asymptotics for multi-dimensional non-homogeneous random walks with asymptotically zero drift
Markov chains with heavy-tailed increments and asymptotically zero drift
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