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Some exact distributions of a last one-sided exit time in the simple random walk
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- Journal:
- Journal of Applied Probability / Volume 23 / Issue 2 / June 1986
- Published online by Cambridge University Press:
- 14 July 2016, pp. 332-340
- Print publication:
- June 1986
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- Article
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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).
, where sup Ø= 0, is given for the case that λ > 0 and μ+ λ= 