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arXiv:1610.03415 [math.PR]AbstractReferencesReviewsResources

The strong Feller property for singular stochastic PDEs

Martin Hairer, Jonathan Mattingly

Published 2016-10-11Version 1

We show that the Markov semigroups generated by a large class of singular stochastic PDEs satisfy the strong Feller property. These include for example the KPZ equation and the dynamical $\Phi^4_3$ model. As a corollary, we prove that the Brownian bridge measure is the unique invariant measure for the KPZ equation with periodic boundary conditions.

Categories: math.PR, math-ph, math.AP, math.MP
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