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July 2001 Stochastic Sub-Additivity Approach to the Conditional Large Deviation Principle
Zhiyi Chi
Ann. Probab. 29(3): 1303-1328 (July 2001). DOI: 10.1214/aop/1015345604


Given two Polish spaces $A_X$ and $A_Y$, let $\rho : A_X \times A_Y \to \mathbb{R}^d$ be a bounded measurable function. Let $X = {X_n : n \geq 1}$ and $Y = {Y_n : n \geq 1}$ be two independent stationary processes on $A_X^{\infty}$ and $A_Y^{\infty}$, respectively. The article studies the large deviation principle (LDP) for $n^{-1} \sum_{k=1}^n \rho(X_k, Y_k)$, 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 $n^{-1} \sum_{k=1}^n \rho(x_k, Y_k)$ satisfy the conditional LDP with a non-random convex rate funcion. Conditions for the rate function to be non-trivial (that is, not $0/\infty$ function) are also given.


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Zhiyi Chi. "Stochastic Sub-Additivity Approach to the Conditional Large Deviation Principle." Ann. Probab. 29 (3) 1303 - 1328, July 2001.


Published: July 2001
First available in Project Euclid: 5 March 2002

zbMATH: 1018.60026
MathSciNet: MR1872744
Digital Object Identifier: 10.1214/aop/1015345604

Primary: 60F10
Secondary: 94A34

Keywords: Conditional large deviation principle , mixing conditions , stochastic approximate subadditivity

Rights: Copyright © 2001 Institute of Mathematical Statistics


Vol.29 • No. 3 • July 2001
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