Liouville theorems for non-local operators

DOI10.1016/j.jfa.2004.04.001zbMath1063.31003OpenAlexW2024292523MaRDI QIDQ705981

Enrico Priola, Zabczyk, Jerzy

Publication date: 16 February 2005

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

Full work available at URL: https://doi.org/10.1016/j.jfa.2004.04.001

zbMATH Keywords

stochastic equationsnon-local operatorsLiouville theoremharmonic functionsLévy noise

Mathematics Subject Classification ID

Related Items (30)

Harnack inequality and Liouville-type theorems for Ornstein-Uhlenbeck and Kolmogorov operators ⋮ On the Liouville property for fully nonlinear equations with superlinear first-order terms ⋮ Davie's type uniqueness for a class of SDEs with jumps ⋮ Integro-PDE in Hilbert spaces: existence of viscosity solutions ⋮ Hardy-Littlewood-Sobolev inequalities for a class of non-symmetric and non-doubling hypoelliptic semigroups ⋮ Liouville results for fully nonlinear equations modeled on Hörmander vector fields. I: The Heisenberg group ⋮ On the infinitesimal generators of Ornstein-Uhlenbeck processes with jumps in Hilbert space ⋮ Global \(L^{p}\) estimates for degenerate Ornstein-Uhlenbeck operators ⋮ Successful couplings for a class of stochastic differential equations driven by Lévy processes ⋮ A sharp Liouville theorem for elliptic operators ⋮ Uniqueness for integro-PDE in Hilbert spaces ⋮ The Liouville theorem and linear operators satisfying the maximum principle ⋮ On the coupling property and the Liouville theorem for Ornstein-Uhlenbeck processes ⋮ Potential theory of infinite dimensional Lévy processes ⋮ Coupling for Ornstein-Uhlenbeck processes with jumps ⋮ On smoothing properties of transition semigroups associated to a class of SDEs with jumps ⋮ Liouville theorems for a class of linear second-order operators with nonnegative characteristic form ⋮ Weighted \(L^p\)-Liouville theorems for hypoelliptic partial differential operators on Lie groups ⋮ Estimates of the derivatives for parabolic operators with unbounded coefficients ⋮ Liouville theorems for non-local operators ⋮ Flow of diffeomorphisms for SDEs with unbounded Hölder continuous drift ⋮ Gradient estimates for diffusion semigroups with singular coefficients ⋮ Structural properties of semilinear SPDEs driven by cylindrical stable processes ⋮ An intrinsic Liouville theorem for degenerate parabolic equations ⋮ A Liouville theorem for Lévy generators ⋮ On bounded solutions to convolution equations ⋮ Regular dependence on initial data for stochastic evolution equations with multiplicative Poisson noise ⋮ Gradient formula for transition semigroup corresponding to stochastic equation driven by a system of independent Lévy processes ⋮ \(L^p\)-Liouville theorems for invariant partial differential operators in \(\mathbb{R}^n\) ⋮ Controllable systems with vanishing energy

Cites Work

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