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December, 1973 A Method for Computing the Asymptotic Limit of a Class of Expected First Passage Times
Walter A. Rosenkrantz
Ann. Probab. 1(6): 1035-1043 (December, 1973). DOI: 10.1214/aop/1176996809

Abstract

The precise asymptotic behavior of certain expected first passage times plays an important role in C. Stone's theory of weak convergence of Markov processes. For a special class of random walks studied by Harris (1952), Lamperti (1962) and Karlin-McGregor (1959) we present a new method, using a maximum principle for a linear second order difference operator, that yields these asymptotic estimates. As a corollary we obtain an alternative proof of Lamperti's (1962) invariance principle.

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Walter A. Rosenkrantz. "A Method for Computing the Asymptotic Limit of a Class of Expected First Passage Times." Ann. Probab. 1 (6) 1035 - 1043, December, 1973. https://doi.org/10.1214/aop/1176996809

Information

Published: December, 1973
First available in Project Euclid: 19 April 2007

zbMATH: 0293.60065
MathSciNet: MR356240
Digital Object Identifier: 10.1214/aop/1176996809

Subjects:
Primary: 60J15
Secondary: 60B10

Keywords: first passage times , maximum principle , weak convergence of Markiov processes

Rights: Copyright © 1973 Institute of Mathematical Statistics

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Vol.1 • No. 6 • December, 1973
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