| In the vast world of contemporary science and society, we can see a model called mathematical of the stochastic process:from the ups and downs of the galaxy,s brightness to the distribution of the spaces, from the Brownian motion of molecule to the transition process of atoms,From the chemical reaction kinetics theory to tele-phone communication theory, from the widespread of rumors to infections preva-lence,from forecasting a market to deciphering a code,its theory and application exist almost everywhere.The first process model which bring forward theoretically and then put into research is Markov chain. Given the current knowledge or information, the past (ie the history state before current) is irrelevant when predicting the future(Ie the future state after the current). Use a popular metaphor to describe it as a rats which is removed of the brain jump move between a number of caves. Because only mice have no memory.The idea born of the moment decision make it jump from a cave to another; When its position is determined,it has nothing to do with its past through when it would next jump up. Markov requires that each time the state transition probability to remain stable.if that changes according to various times, it do not belong to the Markov chain.Markov process gradually stay stable after a long time, and has nothing to do with the initial state, then thewe can say Markov chain is stable.The probability at which time the Markov chain reaches a steady state is the steady-state probability, also called stable.The existence of so called drift criteria,defined by the one-step transition func-tion P,or couched in terms of the expected change,for chains to be stable or un-stable in the various way this is defined.There are four important drift criterion V1,V2,V3,V4.The first drift criteria V1is the development of criteria based on the drift function for both transience and recurrence.The second drift criteria V2also exploit the effect of mean drift,which is stronger on Cc than V1and also requires a bound on the drift away from C.The third drift criteria V3is a generalization of the condition in the V2.As for regular chains,we will find that there is a duality between appropriate solutions to V3and f-regularity.The last drift criteria V4is focus on the f-geometrically regular of set. |
