The Annals of Probability
- Ann. Probab.
- Volume 19, Number 1 (1991), 401-422.
Nonlinear Renewal Theory for Conditional Random Walks
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.
Ann. Probab., Volume 19, Number 1 (1991), 401-422.
First available in Project Euclid: 19 April 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60K05: Renewal theory
Secondary: 60K40: Other physical applications of random processes 62J15: Paired and multiple comparisons
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