Harnack Inequalities for Stochastic Equations Driven by Lévy Noise

Abstract

By using coupling argument and regularization approximations of the underlying subordinator, dimension-free Harnack inequalities are established for a class of stochastic equations driven by a Lévy noise containing a subordinate Brownian motion. The Harnack inequalities are new even for linear equations driven by Lévy noise, and the gradient estimate implied by our log-Harnack inequality considerably generalizes some recent results on gradient estimates and coupling properties derived for Lévy processes or linear equations driven by Lévy noise. The main results are also extended to semi-linear stochastic equations in Hilbert spaces.

15 pages

References in corpus (6)

• Harnack inequality and applications for stochastic generalized porous media equations
• Harnack Inequalities for Functional SDEs with Multiplicative Noise and Applications
• Gradient Estimate for Ornstein-Uhlenbeck Jump Processes
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• Gradient estimates for SDEs Driven by Multiplicative Lévy Noise
• Harnack inequalities for $1$-$d$ stochastic Klein-Gordon type equations
• Fundamental solution of kinetic Fokker-Planck operator with anisotropic nonlocal dissipativity