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arXiv · 1610.03415

The strong Feller property for singular stochastic PDEs

Martin Hairer·Jonathan Mattingly
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Abstract

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.

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Martin Hairer, Jonathan Mattingly. 2016-10-11. The strong Feller property for singular stochastic PDEs. https://arxiv.org/abs/1610.03415

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