The Annals of Probability

Nonlinear Renewal Theory for Conditional Random Walks

Inchi Hu

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Abstract

Herein boundary crossing behavior of conditional random walks is studied. Asymptotic distributions of the exit time and the excess over the boundary are derived. In the course of derivation, two results of independent interest are also obtained: Lemma 4.1 shows that a conditional random walk behaves like an unconditional one locally in a very strong sense. Theorem B.1 describes a class of distributions over which the renewal theorem holds uniformly. Applications are given for modified repeated significance tests and change-point problems.

Article information

Source
Ann. Probab., Volume 19, Number 1 (1991), 401-422.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176990553

Digital Object Identifier
doi:10.1214/aop/1176990553

Mathematical Reviews number (MathSciNet)
MR1085345

Zentralblatt MATH identifier
0727.60103

JSTOR
links.jstor.org

Subjects
Primary: 60K05: Renewal theory
Secondary: 60K40: Other physical applications of random processes 62J15: Paired and multiple comparisons

Keywords
Nonlinear renewal theory renewal theorem boundary crossing probabilities conditional random walks exponential family

Citation

Hu, Inchi. Nonlinear Renewal Theory for Conditional Random Walks. Ann. Probab. 19 (1991), no. 1, 401--422. doi:10.1214/aop/1176990553. https://projecteuclid.org/euclid.aop/1176990553


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