Abstract
Letθ(a) be the first time when the range (Rn;n≧ 0) is equal toa, Rnbeing equal to the difference of the maximum and the minimum, taken at timen, of a simple random walk on ℤ. We compute the g.f. ofθ(a); this allows us to compute the distributions ofθ(a) andRn.We also investigate the asymptotic behaviour ofθ(n),ngoing to infinity.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,Statistics and Probability
Cited by
1 articles.
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1. Symmetric Walks on Paths and Cycles;Mathematics Magazine;2019-08-08