STRONG LIMIT-THEOREMS OF EMPIRICAL DISTRIBUTIONS FOR LARGE SEGMENTAL EXCEEDANCES OF PARTIAL-SUMS OF MARKOV VARIABLES

• 成果类型: Article
• 署名作者: DEMBO, A; KARLIN, S
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176990233
• 发表日期: 1991
• 页码: 1756-1767
• 关键词: additive processes

摘要

Let A1, A2,..., A(n) be generated governed by an r-state irreducible Markov chain and suppose (X(i), U(i)) are real valued independently distributed given the sequence A1, A2,..., A(n), where the joint distribution of (X(i), U(i)) depends only on the values of A(i-1) and A(i) and is of bounded support. Where A0 is started with its stationary distribution, E[X1] < 0 and the existence of a finite cycle C = {A0 = i0,..., A(k) = i(k) = i0} such that Pr{SIGMA-i(m) = 1X(i) > 0, m = 1,..., k; C} > 0 is assumed. For the partial sum realizations where SIGMA-i = k(l)X(i) --> infinity, strong laws are derived for the sums SIGMA-i = k(l)U(i). Examples with r = 2, X is-an-element-of {-1, 1} and the cases of Brownian motion and Poisson process with negative drift are worked out.