Malliavin Calculus for Infinite-Dimensional Systems with Additive Noise

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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.
finial corrections before sending off proofs

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Probability, Mathematical Physics, Analysis of PDEs, 60H15; 60H30; 60H07; 76F20; 76B03; 35J60

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http://salesiana.dossiersoluciones.com/handle/123456789/127107

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0610754
 http://arxiv.org/abs/math/0610754

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arXiv