A TAYLOR APPROXIMATION METHOD OF STOCHASTIC INTEGRO-DIFFERENTIAL EQUATIONS

In this paper, we formulate a general framework of an analytic approximation of the solutions to some It o stochastic integro-differential equations defined on sub-intervals of an arbitrary part of the time-interval [0,1] and connected at successive division points. The integral parts and coefficients of the equation are approximated by their Taylor polynomial which series up to arbitrary derivatives. The suggested approximations converge to the initial solution in the Lp-th norm with some order.