The Spread Of The Markov Chain Approximation And Its Application In The Chemical Master Equation

This paper firstly shows the results about diffusion approximation of discrete-time Markov chain model in 《Theory and Application of Stochastic Processes》 written by Zeev Schuss.He uses a method of Krammer-Moyal expansion(its mathe-matical counterpart is Taylor expansion) to conclude specific forms.necessary con-ditions,advantages and disadvantages of approximation equations for the master equation of the pdf of discrete-time Markov chain with different time scales when jump size tends to zero.Then,these conclusions are generalized to continuous-time&stochastic-waiting time Markov chain model,we can have corresponding results under two kinds of waiting time circumstances.Finally, the basic knowledge about chemical master equation for general biochemical system is briefly introduced,the conclusions we have in second part(Chapter3) are applied in chemical master equa-tion and the corresponding results about diffusion approximation can be obtained when volume of system tends infinity.