Non-linear Renewal Theory with Stationary Perturbations

Abstract

A non-linear renewal theorem is obtained from random walks that are perturbed by an approximately stationary sequence. As corollaries, the limiting joint distribution of the excess over the boundary and last perturbation are obtained along with an approximation to expected first passage times. The results are illustrated by an analysis of a sequential probability ratio test when data are subject to both censoring and staggered entry.

Keywords:

• Asymptotic distributions
• Censoring
• Likelihood function
• Random walks
• Uniform integrability

Acknowledgments

This research was supported by the US Army Research Office under DAAG55-98-0483 and the National Science Foundation under DMS-0102268.

Recommended by T.L. Lai