Derivative Formula and Applications for Degenerate Diffusion Semigroups

Abstract

By using the Malliavin calculus and solving a control problem, Bismut type derivative formulae are established for a class of degenerate diffusion semigroups with non-linear drifts. As applications, explicit gradient estimates and Harnack inequalities are derived.

18 pages

References in corpus (4)

• Formulae for the derivatives of heat semigroups
• Derivative Formula and Harnack Inequality for Linear SDEs Driven by Lévy Processes
• The differentiation of hypoelliptic diffusion semigroups
• Degenerate Fokker-Planck Equations : Bismut Formula, Gradient Estimate and Harnack Inequality

Cited by in corpus (5)

• A Study of a Class of Stochastic Volterra Equations Driven by Fractional Brownian Motion
• Derivative Formula and Harnack Inequality for Degenerate Functional SDEs
• Derivative Formula and Gradient Estimates for Gruschin Type Semigroups
• Log-Harnack Inequality for Gruschin Type Semigroups
• Bismut Formulae and Applications for Functional SPDEs