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Mild Solutions and Harnack Inequality for Functional SPDEs with Dini Drift

The existence and uniqueness of the mild solution for a class of functional SPDEs 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.

preprint2016arXivOpen access
Xing HuangShao-Qin Zhang
math.PR
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Open access2 authors1 topic
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Xing HuangShao-Qin Zhang

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