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The strong Feller property for singular stochastic PDEs

Probability 2017-04-26 v2 Mathematical Physics Analysis of PDEs math.MP

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 Φ34\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.

Keywords

Cite

@article{arxiv.1610.03415,
  title  = {The strong Feller property for singular stochastic PDEs},
  author = {Martin Hairer and Jonathan Mattingly},
  journal= {arXiv preprint arXiv:1610.03415},
  year   = {2017}
}

Comments

updated references and fixed typos