The asymptotic equipartition property of Markov chains in single infinite Markovian environment on countable state space

Small deviation properties concerning arrays of non-homogeneous Markov information sources

“…From the 1970s to the early stages of the 21st century, the AEP for various general stochastic processes was investigated by many studies, such as [8][9][10][11][12][13]. Recently, many scholars, such as Yang (e.g., [14][15][16][17]), Shi (e.g., [3,[18][19][20][21]), Huang [22,23], and Peng [24][25][26], by generalizing the method proposed by [27], [11], and Wang [2,28,29], studied the AEP and the limit properties (including AEP and SLLNs) of some types of Markov chains (such as homogeneous and non-homogeneous; finite state space and infinite state space; and Markov chains indexed by the set of positive integers and tree-indexed Markov chains).…”

The Limit Theorems for Function of Markov Chains in the Environment of Single Infinite Markovian Systems

“…Various research theories about the function of Markov chain in Markovian environments have been proposed, called MCME for short (see [10][11][12][13][14][15]), and the same as theories about the function of Markov chain in random environments, which are called MCRE for short (see [16][17][18]). Exactly, the random environments can be catalogued into different situations, such as in space-time random environments (see [19]), in bi-infinite random environments (see [20]), and in single infinite random environments (see [21]).…”