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The strong Feller property for singular stochastic PDEs
Martin Hairer, Jonathan Mattingly · 2016-10-12 · via math.PR updates on arXiv.org

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 $Φ^4_3$ model. As a corollary, we prove that the Brownian bridge measure is the unique invariant measure for the KPZ equation with periodic boundary conditions.

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