Harnack Inequalities for Functional SDEs with Multiplicative Noise and Applications

Abstract

By constructing a new coupling, the log-Harnack inequality is established for the functional solution of a delay stochastic differential equation with multiplicative noise. As applications, the strong Feller property and heat kernel estimates w.r.t. quasi-invariant probability measures are derived for the associated transition semigroup of the solution. The dimension-free Harnack inequality in the sense of \cite{W97} is also investigated.

22 pages

References in corpus (2)

• Harnack inequality and applications for stochastic generalized porous media equations
• Transportation-Cost Inequalities on Path Space Over Manifolds with Boundary

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• Harnack Inequality for Semilinear spdes with multiplicative noise
• Harnack Inequalities for Ornstein-Uhlenbeck Processes Driven by Lévy Processes
• A Modified log-Harnack inequality and asymptotically strong Feller property