Translator Disclaimer
April 2000 Change of measures for Markov chains and the LlogL theorem for branching processes
Krishna B. Athreya
Author Affiliations +
Bernoulli 6(2): 323-338 (April 2000).

Abstract

Let P(.,.) be a probability transition function on a measurable space ( M,boldM) . Let V(.) be a strictly positive eigenfunction of P with eigenvalue ρ>0. Let P˜ (x,dy)V (y)P(x,dy)ρ V(x). Then P˜ (.,.) is also a transition function. Let Px and P˜ x denote respectively the probability distribution of a Markov chain { X j} 0 with X0=x and transition functions P and P˜ . Conditions for P˜ x to be dominated by Px or to be singular with respect to Px are given in terms of the martingale sequence W n V(X n)/ρ n and its limit. This is applied to establish an LlogL theorem for supercritical branching processes with an arbitrary type space.

Citation

Download Citation

Krishna B. Athreya. "Change of measures for Markov chains and the LlogL theorem for branching processes." Bernoulli 6 (2) 323 - 338, April 2000.

Information

Published: April 2000
First available in Project Euclid: 12 April 2004

zbMATH: 0969.60076
MathSciNet: MR2001G:60202

Rights: Copyright © 2000 Bernoulli Society for Mathematical Statistics and Probability

JOURNAL ARTICLE
16 PAGES


SHARE
Vol.6 • No. 2 • April 2000
Back to Top