Geodesic
A class of strong limit theorems for countable nonhomogeneous Markov chains on the generalized gambling system
Czechoslovak Mathematical Journal, Tome 59 (2009) no. 1, pp. 23-37.

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In this paper, we study the limit properties of countable nonhomogeneous Markov chains in the generalized gambling system by means of constructing compatible distributions and martingales. By allowing random selection functions to take values in arbitrary intervals, the concept of random selection is generalized. As corollaries, some strong limit theorems and the asymptotic equipartition property (AEP) theorems for countable nonhomogeneous Markov chains in the generalized gambling system are established. Some results obtained are extended.
Classification : 60F15, 60G42, 60J10
Keywords: local convergence theorem; stochastic adapted sequence; martingale 
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     title = {A class of strong limit theorems for countable nonhomogeneous {Markov} chains on the generalized gambling system},
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Wang, Kangkang. A class of strong limit theorems for countable nonhomogeneous Markov chains on the generalized gambling system. Czechoslovak Mathematical Journal, Tome 59 (2009) no. 1, pp. 23-37. http://geodesic.mathdoc.fr/item/CMJ_2009__59_1_a1/