Mosco convergence of Dirichlet forms in infinite dimensions with changing reference measures

DOI10.1016/j.jfa.2005.06.002zbMath1093.31007OpenAlexW2070388733MaRDI QIDQ813930

Alexander V. Kolesnikov

Publication date: 2 February 2006

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

Full work available at URL: https://doi.org/10.1016/j.jfa.2005.06.002

zbMATH Keywords

Mosco convergenceconvergence of stochastic processesDirichlet formsGibbs measuresGaussian measuresGibbs state\(\Gamma\)-convergenceconvergence of processes

Mathematics Subject Classification ID

Dirichlet forms (31C25) Probabilistic potential theory (60J45) Measures and integration on abstract linear spaces (46G12) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20) Probability theory on linear topological spaces (60B11)

Related Items

Dynamical universality for random matrices, The Dirichlet-Ferguson diffusion on the space of probability measures over a closed Riemannian manifold, Fractional equations via convergence of forms, A Dirichlet form approach to MCMC optimal scaling, Unnamed Item, Stochastic Heat Equations with Values in a Manifold via Dirichlet Forms, On the closability and convergence of Dirichlet forms, Weak convergence of \(n\)-particle systems using bilinear forms, Discrete approximation of symmetric jump processes on metric measure spaces, A skew stochastic heat equation, Singular perturbations to semilinear stochastic heat equations, Mosco type convergence of bilinear forms and weak convergence of \(n\)-particle systems, A Random String with Reflection in a Convex Domain, Weak convergence of diffusion processes on Wiener space, Mosco convergence of nonlocal to local quadratic forms, Non-local Markovian symmetric forms on infinite dimensional spaces. I: The closability and quasi-regularity, Variational convergence over metric spaces, Particle approximation of the Wasserstein diffusion, Mosco-convergence and Wiener measures for conductive thin boundaries, Condensation of SIP particles and sticky Brownian motion, Approximation of partial differential equations on compact resistance spaces, Homogenization of Symmetric Stable-like Processes in Stationary Ergodic Media, Fréchet differentiable drift dependence of Perron–Frobenius and Koopman operators for non-deterministic dynamics, Convergence of nonlinear semigroups under nonpositive curvature

Cites Work

• Unnamed Item
• Unnamed Item
• Convergence of Dirichlet forms and associated Schrödinger operators
• Uniqueness of generalized Schrödinger operators and applications
• Tightness of general \(C_{1,p}\) capacities on Banach space
• Introduction to the theory of (non-symmetric) Dirichlet forms
• Gibbs measures and phase transitions
• Random fields
• Convergence of non-symmetric forms
• Differentiable measures and the Malliavin calculus
• Uniqueness of generalized Schrödinger operators. II
• Composite media and asymptotic Dirichlet forms
• Dirichlet forms and symmetric Markov processes
• An introduction to \(\Gamma\)-convergence
• Ergodicity for the stochastic dynamics of quasi-invariant measures with applications to Gibbs states
• Weak convergence of symmetric diffusion processes
• Convergence of operator semigroups generated by elliptic operators
• On closability of classical Dirichlet forms.
• BV functions and distorted Ornstein Uhlenbeck processes over the abstract Wiener space
• Convergence of local type Dirichlet forms to a non-local type one
• Classical Dirichlet forms on topological vector spaces --- closability and a Cameron-Martin formula
• Dirichlet operators via stochastic analysis
• Analysis on local Dirichlet spaces. II: Upper Gaussian estimates for the fundamental solutions of parabolic equations
• Entropy, reversible diffusion processes and Markov uniqueness
• On weak convergence of diffusion processes generated by energy forms
• Convergence of distorted Brownian motions and singular Hamiltonians
• Uniqueness and non-uniqueness of semigroups generated by singular diffusion operators
• A priori estimates for symmetrizing measures and their applications to Gibbs states
• Convergence of spectral structures: a functional analytic theory and its applications to spectral geometry
• On a martingale method for symmetric diffusion processes and its applications
• On the small balls problem for equivalent Gaussian measures
• Weighted Sobolev spaces
• Note on Convergence of Dirichlet Processes
• Analysis on local Dirichlet spaces. I. Recurrence, conservativeness and Lp-Liouville properties.
• Finite dimensional approximation of diffusion processes on infinite dimensional spaces
• Convergence of non-symmetric dirichlet processes
• CLOSURE OF THE SET OF DIFFUSION FUNCTIONALS WITH RESPECT TO THE MOSCO-CONVERGENCE
• Convergence of Dirichlet forms with changing speed measures on ℝ d
• Weighted Norm Inequalities for the Hardy Maximal Function
• On the space of BV functions and a related stochastic calculus in infinite dimensions