Tail probabilities of a random walk on an interval

Ewa M. Kubicka, Grzegorz Kubicki, Małgorzata Kuchta and Michał Morayne

Communications in Statistics - Theory and Methods, 2021, vol. 50, issue 9, 2161-2169

Abstract: If a random walk starts at the center of a symmetric discrete interval I={−r,…,−1,0,1,…,r} and we condition on being in I until a given time t, then for any fixed s,0≤s≤r, the probability that at time t the random walk is in the tail {−r,…,−s}∪{s,…,r} is non decreasing in t if we assume that either t is always even or t is always odd.

Date: 2021
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DOI: 10.1080/03610926.2019.1662044

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