Harnack Inequalities for Functional SDEs with Multiplicative Noise and Applications

Details Harnack Inequalities for Functional SDEs with Multiplicative Noise and Applications Harnack Inequalities for Functional SDEs with Multiplicative Noise and Applications

2010-12-28

arxiv.org/abs/1012.5688v2

Mathematics

Probability

22 pages

Scientific paper

10.1214/10-AOP600

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.

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