A strong limit theorem for the average of ternary functions of Markov chains in bi-infinite random environments

作者：Liu, Wei^*; Ma, Chaoqun; Li, Yingqiu; Wang, Suming

来源：Statistics & Probability Letters, 2015, 100: 12-18.

DOI：10.1016/j.spl.2015.01.029

• Bi-infinite random environment
• Markov chain
• Strong limit
• Conditional relative entropy density

We consider strong limit theorems for Markov chains in bi-infinite random environments. We first give a new proof of a strong limit theorem of Liu and Yang (1995) on the average of functions of non-homogeneous Markov chains by constructing a nonnegative martingale. As corollaries, for a Markov chain in a bi-infinite random environment, we obtain strong limit theorems for the conditional relative entropy and for the number of times that the Markov chain and related processes reach a given point.

• 出版日期2015-5
• 单位东莞理工学院; 长沙理工大学; 湖南大学