APPROXIMATION THEOREMS BASED ON RANDOM PARTITIONS FOR STOCHASTIC DIFFERENTIAL EQUATION AND THEIR APPLICATIONS

This kind of problems is discussed:When we use certain smooth approximations of the Brownian motion W as substitutes for it in stochastic line integral and stochastic differential equation,do these resultant integrals and solutions converge to the original one?The corresponding approximation theoroms for two kinds of apprximations are proved,which are wider than those discussed in[1].Some limit theorems about stochastic line integral and solutions of stochastic differential equations with respect to random walks are obtained by using the idea of“embeding a random walk into the Brownian motion”first proposed by A.V.Skorohod.It seems to be remarkable that the method used here is not only effective for the one dimensional case,but also for the multi-dimensional case.