Harnack and Shift Harnack Inequalities for Degenerate (Functional) SPDEs with Singular Drifts

2019/04/06 by Huang, Xing, Lyu, Wujun
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1904.03369

Abstract

The existence and uniqueness of the mild solutions for a class of degenerate functional SPDEs are obtained, where the drift is assumed to be Hölder-Dini continuous. Moreover, the non-explosion of the solution is proved under some reasonable conditions. In addition, the Harnack is derived by the coupling by change of measure. Finally, the shift Harnack inequality is obtained for the equations without delay, which is new even in the non-degenerate case.

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