## The Annals of Probability

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

Carolyn Schroeder

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176989265

Digital Object Identifier
doi:10.1214/aop/1176989265

Mathematical Reviews number (MathSciNet)
MR1217563

Zentralblatt MATH identifier
0781.60024

JSTOR
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. https://projecteuclid.org/euclid.aop/1176989265