Malliavin calculus for infinite-dimensional systems with additive noise


Journal Article

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 dynamics, we develop in this setting a partial counterpart of Hörmander's classical theory of Hypoelliptic operators. 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 a Stochastic Reaction Diffusion Equation and the Stochastic 2D Navier-Stokes System. © 2007 Elsevier Inc. All rights reserved.

Full Text

Duke Authors

Cited Authors

  • Bakhtin, Y; Mattingly, JC

Published Date

  • August 15, 2007

Published In

Volume / Issue

  • 249 / 2

Start / End Page

  • 307 - 353

Electronic International Standard Serial Number (EISSN)

  • 1096-0783

International Standard Serial Number (ISSN)

  • 0022-1236

Digital Object Identifier (DOI)

  • 10.1016/j.jfa.2007.02.011

Citation Source

  • Scopus