A dynamical approximation for stochastic partial differential equations

Details A dynamical approximation for stochastic partial differential equations A dynamical approximation for stochastic partial differential equations

2006-07-03

arxiv.org/abs/math/0607050v2

J. Math. Phys., 2007

Mathematics

Dynamical Systems

28 pages, no figures

Scientific paper

Random invariant manifolds often provide geometric structures for understanding stochastic dynamics. In this paper, a dynamical approximation estimate is derived for a class of stochastic partial differential equations, by showing that the random invariant manifold is almost surely asymptotically complete. The asymptotic dynamical behavior is thus described by a stochastic ordinary differential system on the random invariant manifold, under suitable conditions. As an application, stationary states (invariant measures) is considered for one example of stochastic partial differential equations.

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