Addendum: Limit Theorems for Harris Markov Chains. I

1992 ◽  
Vol 36 (2) ◽  
pp. 426-426
Author(s):  
V. K. Malinovskii
Keyword(s):  
Author(s):  
Pingping Zhong ◽  
Weiguo Yang ◽  
Zhiyan Shi ◽  
Yan Zhang

AbstractThe purpose of this paper is to establish some limit theorems of delayed averages for countable nonhomogeneous Markov chains. The definition of the generalized C-strong ergodicity and the generalized uniformly C-strong ergodicity for countable nonhomogeneous Markov chains is introduced first. Then a theorem about the generalized C-strong ergodicity and the generalized uniformly C-strong ergodicity for the nonhomogeneous Markov chains is established, and its applications to the information theory are given. Finally, the strong law of large numbers of delayed averages of bivariate functions for countable nonhomogeneous Markov chains is proved.


1997 ◽  
Vol 34 (1) ◽  
pp. 24-34 ◽  
Author(s):  
Shoou-Ren Hsiau

This paper establishes a compound Poisson limit theorem for the sum of a sequence of multi-state Markov chains. Our theorem generalizes an earlier one by Koopman for the two-state Markov chain. Moreover, a similar approach is used to derive a limit theorem for the sum of the k th-order two-state Markov chain.


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