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September, 1977 A Nonlinear Renewal Theory with Applications to Sequential Analysis I
T. L. Lai, D. Siegmund
Ann. Statist. 5(5): 946-954 (September, 1977). DOI: 10.1214/aos/1176343950

Abstract

Renewal theory is developed for processes of the form $Z_n = S_n + \xi_n$, where $S_n$ is the $n$th partial sum of a sequence $X_1, X_2, \cdots$ of independent identically distributed random variables with finite positive mean $\mu$ and $\xi_n$ is independent of $X_{n+1}, X_{n+2}, \cdots$ and has sample paths which are slowly changing in an appropriate sense. Applications to sequential analysis are given.

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T. L. Lai. D. Siegmund. "A Nonlinear Renewal Theory with Applications to Sequential Analysis I." Ann. Statist. 5 (5) 946 - 954, September, 1977. https://doi.org/10.1214/aos/1176343950

Information

Published: September, 1977
First available in Project Euclid: 12 April 2007

zbMATH: 0378.62069
MathSciNet: MR445599
Digital Object Identifier: 10.1214/aos/1176343950

Subjects:
Primary: 62L10
Secondary: 60K05

Keywords: Confidence sequences , Renewal theorem , sequential tests

Rights: Copyright © 1977 Institute of Mathematical Statistics

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Vol.5 • No. 5 • September, 1977
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