The Annals of Probability

A Nonlinear Renewal Theory

Cun-Hui Zhang

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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

Permanent link to this document
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
links.jstor.org

Subjects
Primary: 60K05: Renewal theory
Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60] 60J15 62L10: Sequential analysis 62L12: Sequential estimation 62L15: Optimal stopping [See also 60G40, 91A60]

Keywords
Nonlinear renewal theory excess over the boundary uniform integrability expected sample size variance of sample size

Citation

Zhang, Cun-Hui. A Nonlinear Renewal Theory. Ann. Probab. 16 (1988), no. 2, 793--824. doi:10.1214/aop/1176991788. https://projecteuclid.org/euclid.aop/1176991788


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