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February, 1974 A Random Walk with Nearly Uniform $N$-Step Motion
Lawrence E. Myers
Ann. Probab. 2(1): 32-39 (February, 1974). DOI: 10.1214/aop/1176996749


Let $N$ be a strictly positive integer. Motivated by a certain discrete evasion game, we search for a $\{0, 1\}$-valued discrete time stochastic process whose conditional-on-the-past distributions of the sum of the next $N$ terms are as close to uniform as possible. A process is found for which none of the sums ever occurs with conditional probability more than $2e/(N + 1)$. The process is characterized by invariance under interchange of 0 and 1, and its waiting times between successive transitions, which are independently, identically, and uniformly distributed over $\{1,2, \cdots, N + 1\}$.


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Lawrence E. Myers. "A Random Walk with Nearly Uniform $N$-Step Motion." Ann. Probab. 2 (1) 32 - 39, February, 1974.


Published: February, 1974
First available in Project Euclid: 19 April 2007

zbMATH: 0277.60057
MathSciNet: MR368137
Digital Object Identifier: 10.1214/aop/1176996749

Primary: 60G17
Secondary: 60C05 , 60K99

Keywords: $m$-dependent process , $N$-step motion , Random walk

Rights: Copyright © 1974 Institute of Mathematical Statistics


Vol.2 • No. 1 • February, 1974
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