Strong Convergence of Functional Stochastic Differential Equations via the Functional Itô Calculus

Abstract

In general, Malliavin calculus is exploited to construct the Milstein scheme for functional stochastic differential equations due to the appearance of anticipative stochastic integrals. In this paper, by passing the Malliavin calculus, Milstein-type schemes are constructed via the functional Itô calculus for a range of functional stochastic differential equations. As regards the Milstein schemes designed, the strong convergence with the rate 1 is established for functional stochastic differential equations, where the delay measure need not be absolutely continuous with respect to the Lebesgue measure.