Derivative Formula and Harnack Inequality for Linear SDEs Driven by Lévy Processes

Abstract

By using lower bound conditions of the Lévy measure, derivative formulae and Harnack inequalities are derived for linear stochastic differential equations driven by Lévy processes. As applications, explicit gradient estimates and heat kernel inequalities are presented. As byproduct, a new Girsanov theorem for Lévy processes is derived.

25 pages

References in corpus (5)

• Formulae for the derivatives of heat semigroups
• Harnack inequality and applications for stochastic generalized porous media equations
• Coupling property and gradient estimates of Lévy processes via the symbol
• Gradient Estimate for Ornstein-Uhlenbeck Jump Processes
• The Bismut-Elworthy-Li type formulae for stochastic differential equations with jumps

Cited by in corpus (9)

• Harnack Inequalities for Stochastic Equations Driven by Lévy Noise
• Derivative Formula and Applications for Degenerate Diffusion Semigroups
• Exponential Convergence for Semilinear SDEs Driven by Lévy Processes on Hilbert Spaces
• Harnack inequalities for $1$-$d$ stochastic Klein-Gordon type equations
• Derivative Formula and Harnack Inequality for Degenerate Functional SDEs
• Derivative formulas and applications for degenerate SDEs with fractional noises
• A study on the fractional Gruschin type process
• Statistical inference for misspecified ergodic Lévy driven stochastic differential equation models
• Bismut Formulae and Applications for Functional SPDEs