Modern Stochastics: Theory and Applications

In this paper we present a numerical scheme for stochastic differential equations based upon the Wiener chaos expansion. The approximation of a square integrable stochastic differential equation is obtained by cutting off the infinite chaos expansion in chaos order and in number of basis elements. We derive an explicit upper bound for the ${L^{2}}$ approximation error associated with our method. The proofs are based upon an application of Malliavin calculus.

This paper proves the existence and uniqueness of a solution to doubly reflected backward stochastic differential equations where the coefficient is stochastic Lipschitz, by means of the penalization method.