Abstract
This paper concerns a Markov operator T on a space L1, and a Markov process P which defines a Markov operator on a space M of finite signed measures. For T, the paper presents necessary and sufficient conditions for: the existence of invariant probability densities (IPDs) the existence of strictly positive IPDs, and the existence and uniqueness of IPDs. Similar results on invariant probability measures for P are presented. The basic approach is to pose a fixed-point problem as the problem of solving a certain linear equation in a suitable Banach space, and then obtain necessary and sufficient conditions for this equation to have a solution. 1991 Mathematics Subject Classification: 60J05, 47B65, 47N30.
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