High Quality Content by WIKIPEDIA articles! The Malliavin calculus, named after Paul Malliavin, is a theory of variational stochastic calculus. In other words it provides the mechanics to compute derivatives of random variables. The original motivation for the development of the subject was the desirability to provide a stochastic proof that Hormander's condition is sufficient to ensure that the solution of a stochastic differential equation has a density. The calculus also allows important regularity bounds to be obtained for this density. While this original motivation is still very important the calculus has found numerous other applications; for example in stochastic filtering. A useful feature is the ability to perform integration by parts on random variables. This may be used in financial mathematics to compute sensitivities of financial derivatives.

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