Shift Harnack inequality and integration by parts

Authors: Shaoqin Zhang

Publish Date: 2016/03/07

Volume: 11, Issue: 2, Pages: 461-496

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Abstract

Shift Harnack inequality and integration by parts formula are established for semilinear stochastic partial differential equations and stochastic functional partial differential equations by modifying the coupling used by FY Wang Ann Probab 2012 423 994–1019 LogHarnack inequality is established for a class of stochastic evolution equations with nonLipschitz coefficients which includes hyperdissipative NavierStokes/Burgers equations as examples The integration by parts formula is extended to the path space of stochastic functional partial differential equations then a Dirichlet form is defined and the logSobolev inequality is established

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