# A class of strong limit theorems for countable nonhomogeneous Markov chains on the generalized gambling system

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## Abstract

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.

## Keywords

local convergence theorem stochastic adapted sequence martingale## MSC 2000

60F15## Preview

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© Mathematical Institute, Academy of Sciences of Czech Republic 2009