The Annals of Probability

$I$-Projection and Conditional Limit Theorems for Discrete Parameter Markov Processes

Carolyn Schroeder

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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.

Article information

Ann. Probab., Volume 21, Number 2 (1993), 721-758.

First available in Project Euclid: 19 April 2007

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Primary: 60F10: Large deviations
Secondary: 60J05: Discrete-time Markov processes on general state spaces 60G10: Stationary processes 62B10: Information-theoretic topics [See also 94A17] 94A17: Measures of information, entropy

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


Schroeder, Carolyn. $I$-Projection and Conditional Limit Theorems for Discrete Parameter Markov Processes. Ann. Probab. 21 (1993), no. 2, 721--758. doi:10.1214/aop/1176989265.

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