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
Rights: Copyright © 2006, Institute of Mathematical Statistics
