NONLINEAR MARKOV RENEWAL THEORY WITH STATISTICAL APPLICATIONS
成果类型：
Article
署名作者：
MELFI, VF
署名单位：
University of Michigan System; University of Michigan
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/aop/1176989804
发表日期：
1992
页码：
753-771
关键词：
摘要：
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, Y0, Y1,... is a Markov chain with complete separable metric state space; X1, X2,... is a sequence of random variables such that the distribution of X(i) given {Y(j), j greater-than-or-equal-to 0} and {X(j), j not-equal i} depends only on Y(i-1) and Y(i); S(n) = X1 + ... +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.