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April, 1988 A Nonlinear Renewal Theory
Cun-Hui Zhang
Ann. Probab. 16(2): 793-824 (April, 1988). DOI: 10.1214/aop/1176991788


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.


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Cun-Hui Zhang. "A Nonlinear Renewal Theory." Ann. Probab. 16 (2) 793 - 824, April, 1988.


Published: April, 1988
First available in Project Euclid: 19 April 2007

zbMATH: 0643.60067
MathSciNet: MR929079
Digital Object Identifier: 10.1214/aop/1176991788

Primary: 60K05
Secondary: 60G40 , 60J15 , 62L10 , 62L12 , 62L15

Keywords: excess over the boundary , expected sample size , nonlinear renewal theory , uniform integrability , variance of sample size

Rights: Copyright © 1988 Institute of Mathematical Statistics

Vol.16 • No. 2 • April, 1988
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