ON THE APPROXIMATION THEOREM OF THE WONG-ZAKAI TYPE
FOR THE FUNCTIONAL STOCHASTIC DIFFERENTIAL EQUATIONS
Abstract: In this paper we examine the generalization of the Wong-Zakai theorem for the
nonlinear stochastic functional differential equations with values in the space
As the result of the piecewise linear approximation of the -dimensional Wiener process
we obtain an explicit formula for the limit of a sequence of solutions to the ordinary
differential equations with a delay argument; this very limit is a solution to the stochastic
differential equation with a delay argument with the additional term called the Itô correction
term.
2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;
Key words and phrases: -