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April, 1993 $I$-Projection and Conditional Limit Theorems for Discrete Parameter Markov Processes
Carolyn Schroeder
Ann. Probab. 21(2): 721-758 (April, 1993). DOI: 10.1214/aop/1176989265

Abstract

Let $(X, \mathscr{B})$ be a compact metric space with $\mathscr{B}$ the $\sigma$-field of Borel sets. Suppose this is the state space of a discrete parameter Markov process. Let $C$ be a closed convex set of probability measures on $X$. Known results on the asymptotic behavior of the probability that the empirical distributions $\hat{P}_n$ belong to $C$ and new results on the Markov process distribution of $\omega_0, \ldots, \omega_{n - 1}$ under the condition $\hat{P}_n \in C$ are obtained simultaneously through a large deviations estimate. In particular, the Markov process distribution under the condition $\hat{P}_n \in C$ is shown to have an asymptotic quasi-Markov property, generalizing a concept of Csiszar.

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Carolyn Schroeder. "$I$-Projection and Conditional Limit Theorems for Discrete Parameter Markov Processes." Ann. Probab. 21 (2) 721 - 758, April, 1993. https://doi.org/10.1214/aop/1176989265

Information

Published: April, 1993
First available in Project Euclid: 19 April 2007

zbMATH: 0781.60024
MathSciNet: MR1217563
Digital Object Identifier: 10.1214/aop/1176989265

Subjects:
Primary: 60F10
Secondary: 60G10 , 60J05 , 62B10 , 94A17

Keywords: $I$-projection , asymptotically quasi-Markov , large deviations in abstract space

Rights: Copyright © 1993 Institute of Mathematical Statistics

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Vol.21 • No. 2 • April, 1993
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