The unified Taylor–Ito Expansion

The problem of the Taylor–Ito expansion of Ito processes in vicinity of a fixed moment of the time is considered. The Taylor–Ito expansion, which is known in a literature is transformed to the unified Taylor–Ito expansion using the system of the special repeated stohastic Ito integrals with polynomial weight functions. The unified Taylor–Ito expansion include a smaller number of different types of repeated stohastic integrals, than the Taylor–Ito expansion, which is known in a literature. There are the recurrent relations between the coefficients of the unified Taylor–Ito expansion. Therefore the unified Taylor–Ito expansion is more convenient for synthesis of algorithms of numerical solution of stochastic differential Ito equations.