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The ergodic theory of Markov chains in random environments
Authors:Robert Cogburn
Institution:(1) Dept. Math. and Statist, The University of New Mexico, 87131 Albuquerque, New Mexico, USA
Abstract:Summary A general formulation of the stochastic model for a Markov chain in a random environment is given, including an analysis of the dependence relations between the environmental process and the controlled Markov chain, in particular the problem of feedback. Assuming stationary environments, the ergodic theory of Markov processes is applied to give conditions for the existence of finite invariant measure (equilibrium distributions) and to obtain ergodic theorems, which provide results on convergence of products of random stochastic matrices. Coupling theory is used to obtain results on direct convergence of these products and the structure of the tail sgr-field. State properties including classification and communication properties are discussed.
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