Mild Solutions and Harnack Inequality for Functional SPDEs with Dini Drift
Probability
2016-09-07 v1
Abstract
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.
Cite
@article{arxiv.1609.01451,
title = {Mild Solutions and Harnack Inequality for Functional SPDEs with Dini Drift},
author = {Xing Huang and Shao-Qin Zhang},
journal= {arXiv preprint arXiv:1609.01451},
year = {2016}
}