The class of periodic bilinear ARCH model is presented,and some probabilistic properties of the model are discussed,we give several sufficient conditions for the existence of strict periodic stationarity and periodic ergodicity of the model.

Based on the Bowerman’s result about the rate of convergence in Cesaro sense of certain nonhomogeneous Markov chains with the transition matrices converging, certain nonhomogeneous Markov chains in which the transition matrices averagingly converge to a periodic strongly ergodic stochastic (matrice) are studied.

Strict stationary and ergodicity of the multivariate threshold GARCH model;

The Ergodicity of Markov Chains Which Have Only One Instantaneous Points;

Ergodicity for Q-Processes with Markovian Switching

Ergodic in Self-similar Processes and Properties of Related Function;

The Study of Ergodicity for Biased Voter Model, Not Nearest-neighbor Exclusion Process and Hybrid Process;

Utilize the sensitivity and ergodic characteristic of the chaos map,a non-periodic and uniformity distributing multi-chart substitution is designed with multi-iterative equilibrium chaos map.

In this paper we research mainly the ergodic property of the output time series, and we obtain the ergodic state of the output time series in the market economy conditions.

This paper constructs the probability model of multi-value additive clock combined generator,and discusses homogeneous Markov property,ergodic property,strict placidity,numeral character and the property of large numbers of the random variables sequenc with this kind of output sequence.