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

Xing Huang () and Shao-Qin Zhang ()
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Xing Huang: Tianjin University
Shao-Qin Zhang: Central University of Finance and Economics

Journal of Theoretical Probability, 2019, vol. 32, issue 1, 303-329

Abstract: 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; 60H15; 60B10 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10959-018-0830-4

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