Nonlinear renewal theorems for random walks with perturbations of intermediate order

Details Nonlinear renewal theorems for random walks with perturbations of intermediate order Nonlinear renewal theorems for random walks with perturbations of intermediate order

2006-11-22

arxiv.org/abs/math/0611693v1

IMS Lecture Notes--Monograph Series 2006, Vol. 50, 164-175

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/074921706000000671 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/

Scientific paper

10.1214/074921706000000671

We develop nonlinear renewal theorems for a perturbed random walk without assuming stochastic boundedness of centered perturbation terms. A second order expansion of the expected stopping time is obtained via the uniform integrability of the difference between certain linear and nonlinear stopping rules. An intermediate renewal theorem is obtained which provides expansions between the nonlinear versions of the elementary and regular renewal theorems. The expected sample size of a two-sample rank sequential probability ratio test is considered as the motivating example.

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