The unified Taylor-Ito expansion

Abstract

We consider the problem of the Taylor-Ito expansion for Ito processes in a neighborhood of a fixed time moment. The Taylor-Ito expansion known in literature is unified by a canonical system of repeated stochastic Ito integrals with polynomial weight functions. The unified expansion has some computational advantages, such as recurrent relations between the expansion coefficients, ordering of the expansion with respect to smallness of its terms, and a smaller number of applied repeated stochastic integrals of different types. The unified expansion is more convenient in constructing algorithms of numerical solution for stochastic Ito differential equations. Bibliography: 11 titles.