The strong Feller property for singular stochastic PDEs
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.
Type
Journal articlePermalink
https://hdl.handle.net/10161/12996Collections
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Jonathan Christopher Mattingly
James B. Duke Distinguished Professor
Jonathan Christopher Mattingly grew up in Charlotte, NC where he attended Irwin Ave
elementary and Charlotte Country Day. He graduated from the NC School of Science
and Mathematics and received a BS is Applied Mathematics with a concentration in physics
from Yale University. After two years abroad with a year spent at ENS Lyon studying
nonlinear and statistical physics on a Rotary Fellowship, he returned to the US to
attend Princeton University where he obtained a PhD in Applied and
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