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April, 1976 Central Terms of Markov Walks
L. E. Myers
Ann. Probab. 4(2): 313-318 (April, 1976). DOI: 10.1214/aop/1176996136

Abstract

A $\{0, 1\}$-valued discrete time stochastic process $\beta = \{\beta_n\}^\infty_{n=1}$ will be referred to simply as a walk. The notion of central (modal) term of a binomial distribution is generalized to the conditional-on-the-past distributions of $N$th partial sums of walks. The emphasis here is placed on the smallest possible central term $V_A(N)$ within a given class $A$ of walks. If $A$ consists of (i) all walks, (ii) all stationary independent walks, (iii) all stationary Markov walks which are invariant under interchange of 0 and 1, then, respectively, (i) $\{N \cdot V_A(N)\}^\infty_{N=1}$, (ii) $\{N^{\frac{1}{2}} \cdot V_A(N)\}^\infty_{N=1}$, (iii) $\{N \cdot V_A(N)/(\log N)^{\frac{1}{2}}\}^\infty_{N=2}$ are bounded sequences which are bounded away from zero.

Citation

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L. E. Myers. "Central Terms of Markov Walks." Ann. Probab. 4 (2) 313 - 318, April, 1976. https://doi.org/10.1214/aop/1176996136

Information

Published: April, 1976
First available in Project Euclid: 19 April 2007

zbMATH: 0348.60052
MathSciNet: MR423539
Digital Object Identifier: 10.1214/aop/1176996136

Subjects:
Primary: 60G17
Secondary: 60C05, 60G25, 60J10, 62M20

Rights: Copyright © 1976 Institute of Mathematical Statistics

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Vol.4 • No. 2 • April, 1976
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