INVARIANT MEASURES FOR STOCHASTIC HEAT EQUATIONS
Gianmario Tessitore
Jerzy Zabczyk
Abstract: The paper is concerned with the asymptotic behaviour of solutions to the nonlinear
stochastic heat equations, with spatially homogeneous noise, in the whole space. Sufficient
conditions for the existence of invariant measures, in weighted spaces of locally
square-integrable functions, are given.
For linear equations with multiplicative noise an invariant measure, supported by positive
functions, is constructed. The existence of a stationary solution to the vector Burgers
equations is obtained as an application of the general theory.
2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;
Key words and phrases: -