Some exact distributions of a last one-sided exit time in the simple random walk
- 1 June 1986
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 23 (2) , 332-340
- https://doi.org/10.2307/3214177
Abstract
For each positive integer n, let Sn be the nth partial sum of a sequence of i.i.d. random variables which assume the values +1 and −1 with respective probabilities p and 1 – p, having mean μ= 2p − 1. The exact distribution of the random variable , where sup Ø= 0, is given for the case that λ > 0 and μ+ λ= k/(k + 2) for any non-negative integer k. Tables to the 99.99 percentile of some of these distributions, as well as a limiting distribution, are given for the special case of a symmetric simple random walk (p = 1/2).Keywords
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