## The Annals of Probability

### A Nonlinear Renewal Theory

Cun-Hui Zhang

#### Abstract

Let $T$ be the first time that a perturbed random walk crosses a nonlinear boundary. This paper concerns the approximations of the distribution of the excess over the boundary, the expected stopping time $ET$ and the variance of the stopping time $\operatorname{Var}(T)$. Expansions are obtained by using linear renewal theorems with varying drift.

#### Article information

Source
Ann. Probab., Volume 16, Number 2 (1988), 793-824.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176991788

Digital Object Identifier
doi:10.1214/aop/1176991788

Mathematical Reviews number (MathSciNet)
MR929079

Zentralblatt MATH identifier
0643.60067

JSTOR