Let P(.,.) be a probability transition function on a measurable space . Let V(.) be a strictly positive eigenfunction of P with eigenvalue ρ>0. Let Then is also a transition function. Let Px and denote respectively the probability distribution of a Markov chain with X0=x and transition functions P and . Conditions for to be dominated by Px or to be singular with respect to Px are given in terms of the martingale sequence and its limit. This is applied to establish an LlogL theorem for supercritical branching processes with an arbitrary type space.
"Change of measures for Markov chains and the LlogL theorem for branching processes." Bernoulli 6 (2) 323 - 338, April 2000.