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Limit theorems for first-passage times in linear and non-linear renewal theory

Published online by Cambridge University Press:  01 July 2016

S. P. Lalley
S. P. Lalley*
Affiliation:
Stanford University
*
∗Present address: Department of Statistics, Columbia University, New York, NY 10027, USA.
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Abstract

A local limit theorem for is obtained, where τ a is the first time a random walk Sn with positive drift exceeds a. Applications to large-deviation probabilities and to the crossing of a non-linear boundary are given.

Keywords

LOCAL LIMIT THEOREMLARGE DEVIATIONSNON-LINEAR BOUNDARYREPEATED SIGNIFICANCE TEST
Type
Research Article
Information
Advances in Applied Probability , Volume 16 , Issue 4 , December 1984 , pp. 766 - 803
Copyright
Copyright © Applied Probability Trust 1984 

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