Mild Solutions and Harnack Inequality for Functional Stochastic Partial Differential Equations with Dini Drift

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Abstract

The existence and uniqueness of a mild solution for a class of functional stochastic partial differential equations with multiplicative noise and a locally Dini continuous drift are proved. In addition, under a reasonable condition the solution is non-explosive. Moreover, Harnack inequalities are derived for the associated semigroup under certain global conditions, which is new even in the case without delay.

Keywords

Functional SPDEs Mild solution Dini continuous Pathwise uniqueness Harnack inequality 

Mathematics Subject Classification (2010)

60H15 60B10 

Notes

Acknowledgements

The authors would like to thank Professor Feng-Yu Wang and Jianhai Bao for corrections and helpful comments.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Center for Applied MathematicsTianjin UniversityTianjinChina
  2. 2.School of Statistics and MathematicsCentral University of Finance and EconomicsBeijingChina

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