Random Evolutions Processes Induced by Discrete Time Markov Chains

Manuel Keepler

Abstract: Research on the random evolution of a family of semigroups induced by a finite-state, continuous-time, stationary Markov chain was begun by Griego and Hersh in 1969. Subsequently limit theorems and applications for random evolutions have appeared in many places and the theory of random evolutions has been extended and generalized in many directions. In this paper, we extend the theory of random evolutions to discrete time Markov chains. Also, we use the idea of a reversed Markov chain to exhibit subtle connections between forward and backward random evolutions. Aside from their probabilistic significance, the results contribute to the general theory of discrete semigroups.

Keywords: Random evolution; Markov chain; semigroups of operators; stochastic initial value problem.

Classification (MSC2000): 47D05, 47G05; 60F05, 60J25

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