随机环境马氏链下熵的极值问题的研究

The Problem of Extreme Value about Entropy on Markov Chain in Random Environments

在随机环境中马氏链一般理论的研究中,通常要用到随机环境中马氏链与马氏双链间的相互关系.在此基础上,主要探讨了随机环境中马氏链下熵,维数的相关定义,并借助此关系讨论随机环境马氏链下有关熵的不等式的极值问题,获得了相关的结论.

As branches of stochastic process, Markov chains in random environments were developed in 1970s. They have deep realistic background and intensive application. In the study of Markov chains in random environments, we often make use of the relations of Markov chains in random environments and joint Markov chains. Based on the previous works, we study relations among Markov chains in random en- vironments, joint Markov chains and original course. In this paper, on the basis of previous work, we mainly discuss the Markov chains in random environments, entropy, dimension and the relevant definition. This relationship is used to discuss the inequality extreme value problem, and a conclusion is obtained.