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Abstract
R. Cogburn investigated in a series of papers the problem of the existence of invariant measures for Markov processes with random transition probabilities. In this dissertation, we discuss several problems involving Markov processes discussed by Cogburn.
Chapter 1 contains several sufficient conditions for the existence of invariant measures in Cogburn's model. Problems concerning weak ergodicity and weak independence are also discussed.
In Chapter 2, we generalize Cogburn's model to a locally compact state space. A sufficient condition under which there exists a $\sigma$-finite and locally finite invariant measure is given.
In Chapter 3 of this dissertation, to illustrate Markov processes (under Cogburn's model), we consider iterated function systems induced by a number of contractive affine maps on R$\sp{d}$ and discuss left and right attractors for these function systems in the context of invariant probability measures for the system.
