Malliavin's Calculus and Stochastic Integral Representations of Functionals of Diffusion Processes.
Abstract
The recent invention of the so-called Malliavin calculus has led to new advances in the analysis of functionals of Brownian motion. Basically, the Malliavin calculus is a method for integrating by parts in function space and with respect to Wiener measure. One version of the theory can be developed through the use of the Clark-Haussmann formulas (Bismut). Another approach uses a second-order, self-adjoint operator on functionals and the natural concept of differentiation in Wiener space, the H-derivative. In this paper, the authors show that this second form of Malliavin's calculus leads to a very simple derivation of Clark's integral representation. This demonstrates the equivalence of the two approaches to Malliavin's calculus and leads to a nice interpretation of Clark's formula.
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 1983
- Accession Number
- ADA127726
Entities
People
- Daniel Ocone
Organizations
- University of Wisconsin–Madison