Harnack Inequalities and Applications for Multivalued Stochastic Evolution Equations

Details Harnack Inequalities and Applications for Multivalued Stochastic Evolution Equations Harnack Inequalities and Applications for Multivalued Stochastic Evolution Equations

2009-08-25

arxiv.org/abs/0908.3630v1

Mathematics

Probability

18 pages

Scientific paper

By the method of coupling and Girsanov transformation, Harnack inequalities [F.-Y. Wang, 1997] and strong Feller property are proved for the transition semigroup associated with the multivalued stochastic evolution equation on a Gelfand triple. The concentration property of the invariant measure for the semigroup is investigated. As applications of Harnack inequalities, explicit upper bounds of the $L^p$-norm of the density, contractivity, compactness and entropy-cost inequality for the semigroup are also presented.

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