Potential theory of infinite dimensional Lévy processes

DOI10.1016/j.jfa.2011.07.016zbMath1252.60062arXiv1007.2379OpenAlexW2963248791MaRDI QIDQ647599

Michael Roeckner, Lucian Beznea, Aurel Cornea

Publication date: 24 November 2011

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

Full work available at URL: https://arxiv.org/abs/1007.2379

zbMATH Keywords

Dirichlet problemLyapunov functioncapacitypolar setinfinite dimensional Brownian motionabstract Wiener spaceexscessive functionsLévy process on Hilbert space

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Applications of stochastic analysis (to PDEs, etc.) (60H30) Probabilistic potential theory (60J45)

Related Items (8)

An equivalence between the Dirichlet and the Neumann problem for the Laplace operator ⋮ Applications of compact superharmonic functions: path regularity and tightness of capacities ⋮ Some singular sample path properties of a multiparameter fractional Brownian motion ⋮ \(h\)-transform of Doob and nonlocal branching processes ⋮ From resolvents to càdlàg processes through compact excessive functions and applications to singular SDE on Hilbert spaces ⋮ Measure-valued discrete branching Markov processes ⋮ Two theorems on Hunt's hypothesis (H) for Markov processes ⋮ Connections Between the Dirichlet and the Neumann Problem for Continuous and Integrable Boundary Data

Cites Work

• Applications of compact superharmonic functions: path regularity and tightness of capacities
• From resolvents to càdlàg processes through compact excessive functions and applications to singular SDE on Hilbert spaces
• Liouville theorems for non-local operators
• Markoff processes and potentials. I, II, III
• Stopping distributions for right processes
• Quasi-regular Dirichlet forms and \(L^p\)-resolvents on measurable spaces
• Markov processes associated with \(L^{p}\)-resolvents and applications to stochastic differential equations on Hilbert space
• Classical Dirichlet forms on topological vector spaces - the construction of the associated diffusion process
• On the equivalence of three potential principles for right Markov processes
• Semi-polar sets and quasi-balayage
• On Choquet's dichotomy of capacity for Markov processes
• Introduction to the theory of (non-symmetric) Dirichlet forms
• Gaussian measures in Banach spaces
• Generalized Mehler semigroups: The non-Gaussian case
• Potential theory on Hilbert space
• On seminorms and probabilities, and abstract Wiener spaces
• Some regularity properties of diffusion processes on abstract Wiener space
• Séminaire de probabilités. V. Université de Strasbourg
• Harmonic functions on Hilbert space
• ON THE TIGHTNESS OF CAPACITIES ASSOCIATED WITH SUB-MARKOVIAN RESOLVENTS
• On the small balls problem for equivalent Gaussian measures
• Ornstein-Uhlenbeck semigroups in open sets of Hilbert spaces
• A Liouville Theorem for Abstract Wiener Spaces
• Diffusion Semigroups on Abstract Wiener Space
• An Existence Theorem for Second Order Parabolic Equations
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Potential theory of infinite dimensional Lévy processes