Bernoulli

  • Bernoulli
  • Volume 6, Number 2 (2000), 323-338.

Change of measures for Markov chains and the LlogL theorem for branching processes

Krishna B. Athreya

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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.

Article information

Source
Bernoulli, Volume 6, Number 2 (2000), 323-338.

Dates
First available in Project Euclid: 12 April 2004

Permanent link to this document
https://projecteuclid.org/euclid.bj/1081788031

Mathematical Reviews number (MathSciNet)
MR2001g:60202

Zentralblatt MATH identifier
0969.60076

Keywords
change of measures Markov chains martingales measure-valued branching processes

Citation

Athreya, Krishna B. Change of measures for Markov chains and the LlogL theorem for branching processes. Bernoulli 6 (2000), no. 2, 323--338. https://projecteuclid.org/euclid.bj/1081788031


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