The strong Feller property for singular stochastic PDEs
File(s)1610.03415v2.pdf (672.58 KB)
Accepted version
Author(s)
Hairer, M
Mattingly, J
Type
Journal Article
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.
Date Issued
2018-08-01
Date Acceptance
2017-04-23
Citation
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2018, 54 (3), pp.1314-1340
ISSN
0246-0203
Publisher
INST MATHEMATICAL STATISTICS
Start Page
1314
End Page
1340
Journal / Book Title
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES
Volume
54
Issue
3
Copyright Statement
© The Authors
Identifier
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000438376100005&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
Subjects
Science & Technology
Physical Sciences
Statistics & Probability
Mathematics
Strong Feller
Random dynamical systems
Rough stochastic PDEs
Ergodicity
Stochastic quantisation
Girsanov
NAVIER-STOKES EQUATIONS
TIME WHITE-NOISE
DIFFERENTIAL-EQUATIONS
REGULARITY STRUCTURES
INFINITE DIMENSIONS
MALLIAVIN CALCULUS
INVARIANT-MEASURES
KPZ EQUATION
DRIVEN
HYPOELLIPTICITY
Notes
updated references and fixed typos
Publication Status
Published