Non-symmetric perturbations of symmetric Dirichlet forms.
type: Item
instance of: scholarly article
title: Non-symmetric perturbations of symmetric Dirichlet forms.
zbMATH Open document ID: 1065.31009
author: Kazuhiro Kuwae
author: Patrick J. Fitzsimmons
published in: Journal of Functional Analysis
publication date: 2004-03-29T00:00:00Z
review text: Let \(X=(\Omega,{\mathcal F},{\mathcal F}_t,X_t,p^x)\) be a symmetric Markov diffusion process with state space \(E\) and symmetry measure \(m\). Let \(({\mathcal E},{\mathcal D})\) be the associated (strongly local, quasiregular) Dirichlet form. The authors study a class of lower order perturbation of \(({\mathcal E},{\mathcal D})\), obtaining path-space integral representations of the associated semigroups. These representations are a combination of Feynman-Kac and Girsanov formulas. To this end the authors use the Hardy class of smooth measures, which contains the Kato class of smooth measures.
Mathematics Subject Classification ID: 31C25
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 60J57
Mathematics Subject Classification ID: 60J45
zbMATH DE Number: 2062733
zbMATH Keywords: Kato class
zbMATH Keywords: Hardy class
zbMATH Keywords: Feynman-Kac formula
zbMATH Keywords: Girsanov formula
zbMATH Keywords: smooth measure
zbMATH Keywords: positivity preserving form
zbMATH Keywords: local martingale
zbMATH Keywords: Fukushima decomposition
zbMATH Keywords: Nakao divergence
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: j.jfa.2003.10.005
OpenAlex ID: W1982878365
cites work: Brownian motion and harnack inequality for Schrödinger operators
cites work: a general correspondence between\\ Dirichlet forms and right processes
cites work: Quasi-regular Dirichlet forms and Markov processes
cites work: \(L^ p\)-theory of Schrödinger semigroups. II
cites work: Hardy inequalities on non-compact Riemannian manifolds
cites work: Girsanov and Feynman-Kac type transformations for symmetric Markov processes
cites work: From Brownian Motion to Schrödinger’s Equation
cites work: Q4041031
cites work: Q4938492
cites work: Q3915688
cites work: Q4861754
cites work: Absolute continuity of symmetric diffusions
cites work: Hardy's inequality for Dirichlet forms
cites work: On the quasi-regularity of semi-Dirichlet forms
cites work: On the potential theory of symmetric Markov processes
cites work: Dirichlet forms and symmetric Markov processes
cites work: Unique continuation for elliptic operators: A geometric-variational approach
cites work: Measure perturbations of Markovian semigroups
cites work: Optimal Sobolev Inequalities on Complete Riemannian Manifolds with Ricci Curvature Bounded Below and Positive Injectivity Radius
cites work: Existence of invariant measures for diffusion processes on a Wiener space
cites work: Q3874765
cites work: $C_0$-Semigroups in $L^p ({\bf R}^d )$ and $\widehat{C}({\bf R}^d )$ Spaces Generated by the Differential Expression $\Delta + b \cdot \nabla$
cites work: Unique continuation in geometry
cites work: Maximum Principles for Subharmonic Functions Via Local Semi-Dirichlet Forms
cites work: Conservativeness of diffusion processes with drift
cites work: On \(C_ 0\)-semigroups generated by elliptic second order differential expressions on \(L^ p\)-spaces
cites work: Form-bounded perturbations of generators of sub-Markovian semigroups
cites work: On the \(L_{p}\)-theory of \(C_{0}\)-semigroups associated with second-order elliptic operators. II
cites work: Integrability of functionals of Dirichlet processes, probabilistic representations of semigroups, and estimates of heat kernels
cites work: Decomposition of Dirichlet processes and its applications
cites work: Introduction to the theory of (non-symmetric) Dirichlet forms
cites work: Markov Processes Associated With Positivity Preserving Coercive Forms
cites work: On the best constant for Hardy’s inequality in $\mathbb {R}^n$
cites work: Q3995421
cites work: Stochastic calculus for continuous additive functionals of zero energy
cites work: Q3997067
cites work: On some representations of continuous additive functionals locally of zero energy
cites work: PROBABILISTIC REPRESENTATIONS AND HYPERBOUND ESTIMATES FOR SEMIGROUPS
cites work: Lower order perturbations of Dirichlet processes
cites work: Q3872705
cites work: On the \(L_{p}\)-theory of \(C_{0}\)-semigroups associated with second-order elliptic operators. I
cites work: Perturbation of Dirichlet forms by measures
cites work: Markov processes and their functional in duality
cites work: Q5531981
cites work: Generalized Feynman-Kac semigroups, associated quadratic forms and asymptotic properties
DOI: 10.1016/J.JFA.2003.10.005
description: scientific article; zbMATH DE number 2062733