New Itô–Taylor expansions

A new expression for weak truncated Itô–Taylor expansions of functionals of Itô processes is proposed. The new truncated expansion is expressed, as in the ordinary case, in terms of powers of the increments of the variables. A systematic procedure to obtain such expansions and general results in order to avoid some parts of the calculation are presented. As an application, expansions of order up to 6 are derived.