Malliavin Calculus for Infinite-Dimensional Systems with Additive Noise

Details Malliavin Calculus for Infinite-Dimensional Systems with Additive Noise Malliavin Calculus for Infinite-Dimensional Systems with Additive Noise

2006-10-25

arxiv.org/abs/math/0610754v3

Mathematics

Probability

finial corrections before sending off proofs

Scientific paper

We consider an infinite-dimensional dynamical system with polynomial nonlinearity and additive noise given by a finite number of Wiener processes. By studying how randomness is spread by the system we develop a counterpart of Hormander's classical theory in this setting. We study the distributions of finite-dimensional projections of the solutions and give conditions that provide existence and smoothness of densities of these distributions with respect to the Lebesgue measure. We also apply our results to concrete SPDEs such as Stochastic Reaction Diffusion Equation and Stochastic 2D Navier--Stokes System.

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