Non-symmetric perturbations of symmetric Dirichlet forms.

DOI10.1016/j.jfa.2003.10.005zbMath1065.31009OpenAlexW1982878365MaRDI QIDQ1428454

Kazuhiro Kuwae, Patrick J. Fitzsimmons

Publication date: 29 March 2004

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

Full work available at URL: https://doi.org/10.1016/j.jfa.2003.10.005

zbMATH Keywords

Girsanov formulaFeynman-Kac formulaKato classlocal martingalesmooth measureHardy classFukushima decompositionpositivity preserving formNakao divergence

Mathematics Subject Classification ID

Dirichlet forms (31C25) Diffusion processes (60J60) Probabilistic potential theory (60J45) Multiplicative functionals and Markov processes (60J57)

Related Items (18)

ON GIRSANOV AND GENERALIZED FEYNMAN–KAC TRANSFORMATIONS FOR SYMMETRIC MARKOV PROCESSES ⋮ Magnetic Energies and Feynman–Kac–Itô Formulas for Symmetric Markov Processes ⋮ Conservativeness of diffusion processes with drift ⋮ Stochastic calculus for symmetric Markov processes ⋮ Stochastic integration with respect to additive functionals of zero quadratic variation ⋮ Vector analysis for Dirichlet forms and quasilinear PDE and SPDE on metric measure spaces ⋮ Perturbation of symmetric Markov processes ⋮ An integrated version of Varadhan's asymptotics for lower-order perturbations of strong local Dirichlet forms ⋮ Quadratic forms for Feynman-Kac semigroups ⋮ Time-reversal and elliptic boundary value problems ⋮ \(L^p\)-independence of spectral bounds of Feynman-Kac semigroups by continuous additive functionals ⋮ On the generalized Feynman-Kac transformation for nearly symmetric Markov processes ⋮ Strong continuity of generalized Feynman--Kac semigroups: necessary and sufficient conditions ⋮ On general perturbations of symmetric Markov processes ⋮ Approximation of partial differential equations on compact resistance spaces ⋮ Invariant sets and ergodic decomposition of local semi-Dirichlet forms ⋮ Superharmonic functions of Schrödinger operators and Hardy inequalities ⋮ Heat kernel bounds for parabolic equations with singular (form-bounded) vector fields

Cites Work

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• On some representations of continuous additive functionals locally of zero energy
• On the potential theory of symmetric Markov processes
• \(L^ p\)-theory of Schrödinger semigroups. II
• Introduction to the theory of (non-symmetric) Dirichlet forms
• Existence of invariant measures for diffusion processes on a Wiener space
• Integrability of functionals of Dirichlet processes, probabilistic representations of semigroups, and estimates of heat kernels
• Measure perturbations of Markovian semigroups
• Decomposition of Dirichlet processes and its applications
• Dirichlet forms and symmetric Markov processes
• Absolute continuity of symmetric diffusions
• Hardy inequalities on non-compact Riemannian manifolds
• Hardy's inequality for Dirichlet forms
• Girsanov and Feynman-Kac type transformations for symmetric Markov processes
• Quasi-regular Dirichlet forms and Markov processes
• On the \(L_{p}\)-theory of \(C_{0}\)-semigroups associated with second-order elliptic operators. I
• On the \(L_{p}\)-theory of \(C_{0}\)-semigroups associated with second-order elliptic operators. II
• On \(C_ 0\)-semigroups generated by elliptic second order differential expressions on \(L^ p\)-spaces
• Perturbation of Dirichlet forms by measures
• Form-bounded perturbations of generators of sub-Markovian semigroups
• Maximum Principles for Subharmonic Functions Via Local Semi-Dirichlet Forms
• Stochastic calculus for continuous additive functionals of zero energy
• Unique continuation in geometry
• Unique continuation for elliptic operators: A geometric-variational approach
• Brownian motion and harnack inequality for Schrödinger operators
• a general correspondence between\\ Dirichlet forms and right processes
• On the best constant for Hardy’s inequality in $\mathbb {R}^n$
• $C_0$-Semigroups in $L^p ({\bf R}^d )$ and $\widehat{C}({\bf R}^d )$ Spaces Generated by the Differential Expression $\Delta + b \cdot \nabla$
• From Brownian Motion to Schrödinger’s Equation
• Lower order perturbations of Dirichlet processes
• PROBABILISTIC REPRESENTATIONS AND HYPERBOUND ESTIMATES FOR SEMIGROUPS
• Conservativeness of diffusion processes with drift
• Markov Processes Associated With Positivity Preserving Coercive Forms
• Optimal Sobolev Inequalities on Complete Riemannian Manifolds with Ricci Curvature Bounded Below and Positive Injectivity Radius
• Markov processes and their functional in duality
• Generalized Feynman-Kac semigroups, associated quadratic forms and asymptotic properties
• On the quasi-regularity of semi-Dirichlet forms

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