Stochastic sub-additivity approach to the conditional large deviation principle

• 成果类型: Article
• 署名作者: Chi, ZY
• 署名单位: University of Chicago
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1015345604
• 发表日期: 2001
• 页码: 1303-1328
• 关键词: data-compression; asymptotic properties; stationary-processes; waiting-times

摘要

Given two Polish spaces A(X) and A(Y), let rho : A(X) x A(Y) --> R-d be a bounded measurable function. Let X = {X-n : n greater than or equal to 1) and Y = {Y-n: n greater than or equal to 1} be two independent stationary processes on A(X)(infinity) and A(Y)(infinity), respectively. The article studies the large deviation principle (LDP) for n(-1) Sigma(k=1)(n) rho(X-k, Y-k), conditional on X. Based on a stochastic version of approximate subadditivity, it is shown that if Y satisfies certain mixing condition, then for almost all random realization x of X, the laws of n(-1) Sigma(k=1)(n) rho(x(k), Y-k) satisfy the conditional LDP with a non-random convex rate function. Conditions for the rate function to be non-trivial (that is, not 0/infinity function) are also given.