## The Annals of Mathematical Statistics

### Limit Theorems for Markov Transition Functions

Richard Isaac

#### Abstract

New $L_1$ and pointwise limit theorems are proved for the transition functions $P^n(x, E)$ of a Markov process with $\sigma$-finite invariant measure $\pi$ satisfying a recurrence condition. Also given are related results about the operators on functions and measures induced by these transition functions. The method depends upon the application of martingale theorems, and the principal restriction concerns the structure of a certain $\sigma$-field.

#### Article information

Source
Ann. Math. Statist., Volume 43, Number 2 (1972), 621-626.

Dates
First available in Project Euclid: 27 April 2007

https://projecteuclid.org/euclid.aoms/1177692641

Digital Object Identifier
doi:10.1214/aoms/1177692641

Mathematical Reviews number (MathSciNet)
MR300338

Zentralblatt MATH identifier
0278.60048

JSTOR