Stochastic Analysis On Time Scales And Its Applyings

Stochastic process is a mathematical subject which studys statics regularity of stochastic phenomenon dynamically, in which the study objects of stochastic analysis included are mean-square limit,mean-square continuity,mean-square derivative and mean-square integral of the second moment process. Now the study on stochastic process only refers to two special status, namely discrete and continuous states, and the stochastic analysis is the same. The so-called time scales are non-empty closed sets. Discrete state and continuous state are two special examples on time scales.This thesis of Master is composed of three chapters,the main contents of which are studying stochastic analysis and some applyings on time scales. Applying the time scales theory into the second moment process, some relative basic concepts are founded in general states. It is also applied into mean value theorem on time scales, some useful results about mean value theorem of second moment process on time scales are formed. It is a preparation for the study on the stochastic process under the general condition and the stability of stochastic differential equation on time scales.In chapter one, namely introduction of this article, I chiefly introduce the importance of stability of dynamic system , the development of stochastic differential equation and its stability theory, and stochastic pross, especially stochastic analysis in it. In the same time, I also simply introduce the foundation and development of the time scales theory. In the end, we simply introduce the chief job in this article. In chapter two, I simply review and introduce some preparation knowledge which is needed for the chief results of this article. The preparation knowledge include the basic knowledge of the second moment process in stochastic process and the time scales theory.Chapter three is one of the cores of this article, in which I discuss some results of applying the time scales theory into the second moment process in stochastic analysis, chiefly include: mean-square limit on time scales, mean-square continuity on time scales, mean-square derivative on time scales, mean-square integral on time scales.Chapter four is also the core of this article, on the basis of the results got in chapter three, I furtherly apply these results, and get mean value theorem on time scales.In the end, I make a conclusion of this paper and give a plan of the future work.