LOG-HARNACK INEQUALITY FOR STOCHASTIC DIFFERENTIAL EQUATIONS IN HILBERT SPACES AND ITS CONSEQUENCES

Röckner M, Wang F-Y. LOG-HARNACK INEQUALITY FOR STOCHASTIC DIFFERENTIAL EQUATIONS IN HILBERT SPACES AND ITS CONSEQUENCES. Infinite Dimensional Analysis, Quantum Probability and Related Topics. 2010;13(1):27-37.A logarithmic type Harnack inequality is established for the semigroup of solutions to a stochastic differential equation in Hilbert spaces with non-additive noise. As applications, the strong Feller property as well as the entropy-cost inequality for the semigroup are derived with respect to the corresponding distance (cost function)