Log-Harnack Inequality for Stochastic Burgers Equations and Applications

Details Log-Harnack Inequality for Stochastic Burgers Equations and Applications Log-Harnack Inequality for Stochastic Burgers Equations and Applications

2010-09-29

arxiv.org/abs/1009.5948v1

Mathematics

Probability

Scientific paper

By proving an $L^2$-gradient estimate for the corresponding Galerkin approximations, the log-Harnack inequality is established for the semigroup associated to a class of stochastic Burgers equations. As applications, we derive the strong Feller property of the semigroup, the irreducibility of the solution, the entropy-cost inequality for the adjoint semigroup, and entropy upper bounds of the transition density.

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