We show that the set of stationary weak solutions for a class of infinite dimen- sional stochastic differential equations coincides with the set of shift invariant, space-time Gibbs fields for a certain potential. The key step consists in proving the Gibbs variational principle for space-time Gibbs fields.
A Gibbs variational principle in space-time for infinite-dimensional diffusions
DAI PRA, PAOLO;
2002
Abstract
We show that the set of stationary weak solutions for a class of infinite dimen- sional stochastic differential equations coincides with the set of shift invariant, space-time Gibbs fields for a certain potential. The key step consists in proving the Gibbs variational principle for space-time Gibbs fields.
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