Applications of the Malliavin calculus, Part III

Publisher Summary This chapter discusses the application of Malliavin's calculus to various problems in stochastic analysis and the theory of partial differential equations. The chapter examines the regularity estimates on the distribution of functionals to which Malliavin's procedure is applicable. It is shown that solutions of Ito stochastic integral equations are smooth functions in the sense of Malliavin's calculus. The distribution of the solution to a general Ito equation has the same regularity properties as that of a classical diffusion just so long as the coefficients of the white noise are non-degenerate. Any other method, of deducing this result and believing that it is a good example to illustrate the power of Malliavin's calculus, is not known.