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VOL. 50 | 2006 A non-linear Renewal Theorem with stationary and slowly changing perturbations
Dong-Yun Kim, Michael Woodroofe

Editor(s) Jiayang Sun, Anirban DasGupta, Vince Melfi, Connie Page

## Abstract

Non-linear renewal theory is extended to include random walks perturbed by both a slowly changing sequence and a stationary one. Main results include a version of the Key Renewal Theorem, a derivation of the limiting distribution of the excess over a boundary, and an expansion for the expected first passage time. The formulation is motivated by problems in sequential analysis with staggered entry, where subjects enter a study at random times.

## Information

Published: 1 January 2006
First available in Project Euclid: 28 November 2007

zbMATH: 1268.60108
MathSciNet: MR2409552

Digital Object Identifier: 10.1214/074921706000000680

Subjects:
Primary: 60K05

Keywords: excess over the boundary , first passage times , fixed width confidence intervals , repeated likelihood ratio tests , staggered entry