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April, 1974 A Simple proof of a Known Result in Random Walk Theory
Austin J. Lemoine
Ann. Probab. 2(2): 347-348 (April, 1974). DOI: 10.1214/aop/1176996718

Abstract

Let $\{X_n, n \geqq 1\}$ be a stationary independent sequence of real random variables, $S_n = X_1 + \cdots + X_n$, and $\alpha_A$ the hitting time of the set $A$ by the process $\{S_n, n \geqq 1\}$, where $A$ is one of the half-lines $(0, \infty), \lbrack 0, \infty), (-\infty, 0 \rbrack$ or $(-\infty, 0)$. This note provides a simple proof of a known result in random walk theory on necessary and sufficient conditions for $E\{\alpha_A\}$ to be finite. The method requires neither generating functions nor moment conditions on $X_1$.

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Austin J. Lemoine. "A Simple proof of a Known Result in Random Walk Theory." Ann. Probab. 2 (2) 347 - 348, April, 1974. https://doi.org/10.1214/aop/1176996718

Information

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

zbMATH: 0278.60043
MathSciNet: MR356244
Digital Object Identifier: 10.1214/aop/1176996718

Subjects:
Primary: 60J15
Secondary: 60K25

Keywords: hitting times , Random walks

Rights: Copyright © 1974 Institute of Mathematical Statistics

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Vol.2 • No. 2 • April, 1974
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