随机环境马氏链下弱遍历性及其应用

The Properties and Application of Weak Ergodicity on Finite States Markov Chain in Random Environments

假设X是随机环境的马氏链,首先介绍了弱遍历性及相遇关系,讨论了相遇关系的性质,获得了相遇关系的一些结论,进一步地,利用相遇关系与弱遍历性的关系,得到了随机环境马氏链的平均遍历极限,最后,利用随机环境马氏链下极限性质及不变测度,讨论了随机环境马氏链在管理学方面的应用问题,即人员配备问题,获得了经过长时间的市场调节,各网点人员配备会达到均衡φ(.,θ)的结论.

Let X be Markov chains in random environments.In this paper,first of all,we introduce weak ergodicity and meeting relationship,discuss properties of meeting relationship and draw some conclusions about meeting relationship.Further,by the relation between the weak ergodicity and meeting relationship,we obtain the ergodic limit of Markov chains in random environments.Finally,by the limit properties and invariant measure of Markov chains in random environments,we discuss an application on management science and obtain balance about staffing by market regulation.