Strong law of large numbers for discrete-time and continuous-state nonhomogeneous Markov chains;

Based on domestic and international data,the homogeneous and nonhomogeneous poisson theory continuous time discrete state Markov process are used,and the related concepts are given.

In this paper, the convergent conditions in sequence or parallel update mode and the sufficient condition with only one global stable state for Hopfield network model with discrete time and continuous states when its neurons?activation function is non-decreasing (not being strictly monotone increasing) are discussed.

Property of absolute mean strong ergodic for nonhomogeneous Markov Chains;

A strong law of large numbers for mth order countable nonhomogeneous Markov chains;

Strong limit theorems for nonhomogeneous Markov chains

In the study of the strong law of large numbers in probability theory, non-homogeneous Markov chains investigated by many scholars have been correspondingly restricted in their works.

In this paper, the idea of random selection on gambling system is extend to nonhomgenous Markov chains of order 2, and some strong limit theorems on the function of nonhomgenous Markov chains of order 2 is discussed by means of martingale method, as a lemma, some strong limit theorems on random selection are also obtained.