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 $X_1$.
Citation
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
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