Open Access
Translator Disclaimer
January, 1991 Nonlinear Renewal Theory for Conditional Random Walks
Inchi Hu
Ann. Probab. 19(1): 401-422 (January, 1991). DOI: 10.1214/aop/1176990553


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.


Download Citation

Inchi Hu. "Nonlinear Renewal Theory for Conditional Random Walks." Ann. Probab. 19 (1) 401 - 422, January, 1991.


Published: January, 1991
First available in Project Euclid: 19 April 2007

zbMATH: 0727.60103
MathSciNet: MR1085345
Digital Object Identifier: 10.1214/aop/1176990553

Primary: 60K05
Secondary: 60K40 , 62J15

Keywords: boundary crossing probabilities , conditional random walks , exponential family , nonlinear renewal theory , Renewal theorem

Rights: Copyright © 1991 Institute of Mathematical Statistics


Vol.19 • No. 1 • January, 1991
Back to Top