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.
Publié le : 1993-04-14
Classification:
$I$-projection,
large deviations in abstract space,
asymptotically quasi-Markov,
60F10,
60J05,
60G10,
62B10,
94A17
@article{1176989265,
author = {Schroeder, Carolyn},
title = {$I$-Projection and Conditional Limit Theorems for Discrete Parameter Markov Processes},
journal = {Ann. Probab.},
volume = {21},
number = {4},
year = {1993},
pages = { 721-758},
language = {en},
url = {http://dml.mathdoc.fr/item/1176989265}
}
Schroeder, Carolyn. $I$-Projection and Conditional Limit Theorems for Discrete Parameter Markov Processes. Ann. Probab., Tome 21 (1993) no. 4, pp. 721-758. http://gdmltest.u-ga.fr/item/1176989265/