Tail probabilities of a random walk on an interval

If a random walk starts at the center of a symmetric discrete interval and we condition on being in I until a given time t, then for any fixed , the probability that at time t the random walk is in the tail is non decreasing in t if we assume that either t is always even or t is always odd.

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Bibliographic Details
Published in:Communications in statistics. Theory and methods 2021-05, Vol.50 (9), p.2161-2169
Main Authors: Kubicka, Ewa M., Kubicki, Grzegorz, Kuchta, Małgorzata, Morayne, Michał
Format: Article
Language:English
Subjects:
discrete interval
Random walk
tail probabilities
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Description
Summary:If a random walk starts at the center of a symmetric discrete interval and we condition on being in I until a given time t, then for any fixed , the probability that at time t the random walk is in the tail is non decreasing in t if we assume that either t is always even or t is always odd.
ISSN:0361-0926
1532-415X
DOI:10.1080/03610926.2019.1662044