Ergodic For Multiple Nonhomogeneous Markov Chains And Application

Ergodicity is always an interesting and challenging research task in the fields of Markov theory. The ergodic for Markov has extensive application and plays an important role in the areas of biology, numerical calculate, theory of information, automatic command, physics and the service system of public enterprise.In this paper we principally research ergodic for multiple nonhomogeneous Markov chains and application. The notions of the strongly ergodic and weakly ergodic for m order finite nonhomogeneous Markov chains are defined. The conditions under which a m order. finite nonhomogeneous Markov chains possesses the kind of strongly ergodic and weakly ergodic are obtained respectively by applying the relations between multiple Markov chains and Markov chains and C-K equation of the multiple Markov chains. Some results about ergodicity for multiple homogeneous Markov chains are extended to multiple finite nonhomogeneous Markov chains. Based on this, the notions of the strongly ergodic and absolute mean strongly ergodic for m order nonhomogeneous Markov chains are defined and the conditions under which a m order nonhomogeneous Markov chains possesses the kind of strongly ergodic and absolute mean strongly ergodic are researched respectively. In this paper, the notion of the convergence of Cesaro averages for m order nonhomogeneous Markov chains is introduced. Based on this, we prove a convergence theorem for Cesaro averages for m order nonhomogeneous Markov chains, and discuss the application of this theorem on the information theory. Finally, we give the application of multiple Markov chains on the genetic algorithms. Based on describing multiple Markov chains of individuals in the steady state genetic algorithm, we improve the algorithm and prove that the improved steady state genetic algorithm is global convergence, by applying ergodic for multiple finite nonhomogen- eous Markov chains.