The Maximum of an Asymmetric Simple Random Walk with Reflection

2018/08/06 by Steven R. Finch, Finch, Steven R. · 5 citations
Mathematics · Computer Science · #Stochastic processes and statistical mechanics #Advanced Database Systems and Queries #Data Management and Algorithms

paper · pdf · doi:10.48550/arxiv.1808.01830

Abstract

Consider the extreme value of a Bernoulli random walk on the one-dimensional integer lattice, with reflection at 0, over a finite discrete time interval. Only the asymmetric (biased) case is discussed. Asymptotic mean/variance results are given as the time interval length approaches infinity. We similarly solve an elementary traffic light problem from queueing theory.

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