Strong law of large numbers for generalized sample relative entropy of non homogeneous Markov chains

Jie Yang, Weiguo Yang, Zhiyan Shi, Yiqing Li, Bei Wang and Yue Zhang

Communications in Statistics - Theory and Methods, 2018, vol. 47, issue 7, 1571-1579

Abstract: In this paper, we study the strong law of large numbers for the generalized sample relative entropy of non homogeneous Markov chains taking values from a finite state space. First, we introduce the definitions of generalized sample relative entropy and generalized sample relative entropy rate. Then, using a strong limit theorem for the delayed sums of the functions of two variables and a strong law of large numbers for non homogeneous Markov chains, we obtain the strong law of large numbers for the generalized sample relative entropy of non homogeneous Markov chains. As corollaries, we obtain some important results.

Date: 2018
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DOI: 10.1080/03610926.2017.1321770

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