Abstract
Malliavin (1978) introduced new methods for the study of functionals defined on Wiener space. Concepts, such as smoothness and non-degeneracy of maps of Wiener space into Euclidean spaces were studied and regularity of the induced distributions of smooth non-degenerate maps was established through integration by parts formulae. In the beginning, this was limited to Wiener space and could handle solutions of stochastic differential equations driven by Brownian motion and could show that their distributions have smooth densities under appropriate ellipticity or hypo-ellipticity conditions.
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