A nonlinear renewal theory
type: Item
instance of: scholarly article
title: A nonlinear renewal theory
zbMATH Open document ID: 0643.60067
author: Cun-Hui Zhang
published in: The Annals of Probability
publication date: 1988-01-01T00:00:00Z
review text: Let T be the first passage time across a nonlinear boundary for a perturbed random walk. The present paper presents approximations of the distribution of the overshoot, E(T) and Var(T). An important tool in the proofs are renewal theorems for first passage times across horizontal levels for nonperturbed random walks with a drift that is smaller than the drift of the original, nonperturbed random walk and results about uniform integrability of powers of the difference of the two first passage time processes.
Mathematics Subject Classification ID: 60K05
Mathematics Subject Classification ID: 60G40
Mathematics Subject Classification ID: 60G50
Mathematics Subject Classification ID: 62L10
Mathematics Subject Classification ID: 62L15
Mathematics Subject Classification ID: 62L12
zbMATH DE Number: 4048804
zbMATH Keywords: first passage time across a nonlinear boundary
zbMATH Keywords: perturbed random walk
zbMATH Keywords: renewal theorems
zbMATH Keywords: uniform integrability
reviewed by: Allan Gut
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176991788
OpenAlex ID: W2055760790
DOI: 10.1214/AOP/1176991788
description: scientific article; zbMATH DE number 4048804