Open Access
April, 1992 Nonlinear Markov Renewal Theory with Statistical Applications
Vincent F. Melfi
Ann. Probab. 20(2): 753-771 (April, 1992). DOI: 10.1214/aop/1176989804


An analogue of the Lai-Siegmund nonlinear renewal theorem is proved for processes of the form $S_n + \xi_n$, where $\{S_n\}$ is a Markov random walk. Specifically, $Y_0,Y_1,\cdots$ is a Markov chain with complete separable metric state space; $X_1,X_2,\cdots$ is a sequence of random variables such that the distribution of $X_i$ given $\{Y_j, j \geq 0\}$ and $\{X_j, j \neq i\}$ depends only on $Y_{i - 1}$ and $Y_i; S_n = X_1 + \cdots + X_n$; and $\{\xi_n\}$ is slowly changing, in a sense to be made precise below. Applications to sequential analysis are given with both countable and uncountable state space.


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Vincent F. Melfi. "Nonlinear Markov Renewal Theory with Statistical Applications." Ann. Probab. 20 (2) 753 - 771, April, 1992.


Published: April, 1992
First available in Project Euclid: 19 April 2007

zbMATH: 0756.60082
MathSciNet: MR1159572
Digital Object Identifier: 10.1214/aop/1176989804

Primary: 60K05
Secondary: 60J05 , 60K15 , 62L05

Keywords: excess over the boundary , Markov chain , Markov random walk , nonlinear renewal theorem , repeated significance test

Rights: Copyright © 1992 Institute of Mathematical Statistics

Vol.20 • No. 2 • April, 1992
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