APPROXIMATION OF RANDOM INVARIANT MANIFOLDS FOR A STOCHASTIC SWIFT-HOHENBERG EQUATION.

Random invariant manifolds are considered for a stochastic Swift- Hohenberg equation with multiplicative noise in the Stratonovich sense. Using a stochastic transformation and a technique of cut-off function, existence of random invariant manifolds and attracting property of the corresponding random dynamical system are obtained by Lyaponov-Perron method. Then in the sense of large probability, an approximation of invariant manifolds has been investigated and this is further used to describe the geometric shape of the invariant manifolds. [ABSTRACT FROM AUTHOR]