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WROCŁAW UNIVERSITY
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TECHNOLOGY

Contents of PMS, Vol. 12, Fasc. 2,
pages 319 - 334
 

ON THE APPROXIMATION THEOREM OF THE WONG-ZAKAI TYPE FOR THE FUNCTIONAL STOCHASTIC DIFFERENTIAL EQUATIONS

Krystyna Twardowska

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 Rd (d > 1). As the result of the piecewise linear approximation of the m -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: -

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