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The Maximum of an Asymmetric Simple Random Walk with Reflection (1808.01830v2)
Published 6 Aug 2018 in math.HO
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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