Strong uniqueness for both Dirichlet operators and stochastic dynamics to Gibbs measures on a path space with exponential interactions

DOI10.1016/j.jfa.2011.09.023zbMath1256.47027arXiv1006.5590OpenAlexW1996281515MaRDI QIDQ656210

Hiroshi Kawabi, Michael Roeckner, Sergio A. Albeverio

Publication date: 17 January 2012

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1006.5590

zbMATH Keywords

logarithmic Sobolev inequalitypath spaceGibbs measureessential self-adjointnessSPDEstrong uniquenessquantum fieldsDirichlet operator\(L^p\)-uniqueness

Mathematics Subject Classification ID

Markov semigroups and applications to diffusion processes (47D07) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs on infinite-dimensional (e.g., function) spaces (= PDEs in infinitely many variables) (35R15) Stochastic quantization (81S20)

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Along Paths Inspired by Ludwig Streit: Stochastic Equations for Quantum Fields and Related Systems ⋮ A class of Lévy driven SDEs and their explicit invariant measures ⋮ A variational approach to dissipative SPDEs with singular drift ⋮ First order Feynman-Kac formula ⋮ Restricted Markov uniqueness for the stochastic quantization of \(P(\Phi)_{2}\) and its applications ⋮ Local bounds for stochastic reaction diffusion equations ⋮ Strong uniqueness for Dirichlet operators related to stochastic quantization under exponential/trigonometric interactions on the two-dimensional torus ⋮ Small noise asymptotic expansions for stochastic PDE's driven by dissipative nonlinearity and Lévy noise ⋮ On the parabolic and hyperbolic Liouville equations ⋮ Stochastic quantization associated with the \(\exp(\Phi)_2\)-quantum field model driven by space-time white noise on the torus ⋮ The elliptic stochastic quantization of some two dimensional Euclidean QFTs ⋮ Elliptic stochastic quantization ⋮ Well-posedness of monotone semilinear SPDEs with semimartingale noise

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