Stochastic Integrals and Derivatives

B. Rajeev

Abstract

In this talk, we show that an earlier differentiation formula of the author, used to represent any square integrable functional of Brownian motion as a stochastic integral, remains valid for continuous local martingale integrals. The Martingale representation theorem for a process takes the form of a Hilbert space isomorphism between the L_2 space of the process and an appropriate stochastic Sobolev space.