Strong law of large numbers for generalized sample relative entropy of non homogeneous Markov chains. Issue 7 (3rd April 2018)

• Record Type: Journal Article
• Authors: Yang, Jie; Yang, Weiguo; Shi, Zhiyan; Li, Yiqing; Wang, Bei; Zhang, Yue
• Is Part Of: Communications in statistics. Volume 47:Issue 7(2018)
• Page Start: 1571
• Page End: 1579
• Publication Date: 2018-04-03
• Subjects: Generalized sample relative entropy -- non homogeneous Markov chains -- strong law of large numbers.; 94A17 -- 60J10; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2017.1321770
• Languages: English
• ISSNs: 0361-0926

Abstract

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.