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

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.

10 pages

References in corpus (1)

• A transient Markov chain with finitely many cutpoints

Cited by in corpus (1)

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