Green function for gradient perturbation of unimodal Lévy processes in the real line

DOI10.1007/s40840-019-00738-4zbMath1496.60103arXiv1802.01450OpenAlexW2964236756MaRDI QIDQ2305621

G. Żurek, Tomasz Grzywny, Tomasz Jakubowski

Publication date: 11 March 2020

Published in: Bulletin of the Malaysian Mathematical Sciences Society. Second Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1802.01450

zbMATH Keywords

Green functionPoisson kernelunimodal Lévy process\(C^{1,1}\) domain

Mathematics Subject Classification ID

Perturbation theory of linear operators (47A55) Transition functions, generators and resolvents (60J35) Boundary theory for Markov processes (60J50) Integro-differential operators (47G20) Jump processes on general state spaces (60J76)

Related Items (1)

On the mean value property of fractional harmonic functions

Cites Work

• Unnamed Item
• Unnamed Item
• Upper bounds for fundamental solutions to non-local diffusion equations with divergence free drift
• Martin representation and relative Fatou theorem for fractional Laplacian with a gradient perturbation
• Dirichlet heat kernel for unimodal Lévy processes
• Principal eigenvalue of the fractional Laplacian with a large incompressible drift
• Estimates of the Green function for the fractional Laplacian perturbed by gradient
• Majorization, 4G theorem and Schrödinger perturbations
• Hitting times of points and intervals for symmetric Lévy processes
• Estimates of gradient perturbation series
• Dirichlet heat kernel estimates for fractional Laplacian with gradient perturbation
• Excursions away from a regular point for one-dimensional symmetric Lévy processes without Gaussian part
• Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation
• Conditional transformation of drift formula and potential theory for \(\Delta +b(\cdot)\cdot \nabla\)
• The growth of random walks and Levy processes
• On the loss of continuity for super-critical drift-diffusion equations
• Heat kernels of non-symmetric Lévy-type operators
• The estimates of the mean first exit time from a ball for the \(\alpha \)-stable Ornstein-Uhlenbeck processes
• Density and tails of unimodal convolution semigroups
• Estimates of heat kernel of fractional Laplacian perturbed by gradient operators
• On Harnack inequality for \(\alpha\)-stable Ornstein-Uhlenbeck processes
• On Harnack inequality and Hölder regularity for isotropic unimodal Lévy processes
• On some relations between the harmonic measure and the Levy measure for a certain class of Markov processes
• Martin boundary for some symmetric Lévy processes
• Dirichlet heat kernel estimates for rotationally symmetric Lévy processes
• Fractional Laplacian with singular drift
• Gradient estimates of harmonic functions and transition densities for Lévy processes
• Time-dependent Schrödinger perturbations of transition densities
• [https://portal.mardi4nfdi.de/wiki/Publication:3664169 The isoperimetric inequality for isotropic unimodal L�vy processes]
• From Brownian Motion to Schrödinger’s Equation
• Some perturbations of drift-type for symmetric stable processes
• Potential theory of one-dimensional geometric stable processes
• Hölder estimates for advection fractional-diffusion equations
• Green function for gradient perturbation of unimodal L\'{e}vy processes
• Markov Processes, Brownian Motion, and Time Symmetry
• On the Distribution of First Hits for the Symmetric Stable Processes

This page was built for publication: Green function for gradient perturbation of unimodal Lévy processes in the real line