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December, 1972 Estimates of the Rates of Convergence in Limit Theorems for the First Passage Times of Random Walks
Douglas P. Kennedy
Ann. Math. Statist. 43(6): 2090-2094 (December, 1972). DOI: 10.1214/aoms/1177690890

Abstract

Let $T_r$ be the time of first passage to the level $r > 0$ by a random walk with independent and identically distributed steps and mean $\nu \geqq 0$. Estimates are given for the rate at which the distribution of $T_r$, suitably scaled and normalized, converges to the stable distribution with index $\frac{1}{2}$ when $\nu = 0$ and to the normal distribution when $\nu > 0$ as $r \rightarrow \infty$.

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Douglas P. Kennedy. "Estimates of the Rates of Convergence in Limit Theorems for the First Passage Times of Random Walks." Ann. Math. Statist. 43 (6) 2090 - 2094, December, 1972. https://doi.org/10.1214/aoms/1177690890

Information

Published: December, 1972
First available in Project Euclid: 27 April 2007

zbMATH: 0252.60027
MathSciNet: MR365666
Digital Object Identifier: 10.1214/aoms/1177690890

Rights: Copyright © 1972 Institute of Mathematical Statistics

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Vol.43 • No. 6 • December, 1972
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