Distribution-Dependent Stochastic Functional Differential Equations

Xing Huang

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arXiv · 1612.08542

Distribution-Dependent Stochastic Functional Differential Equations

Xing Huang

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Abstract

By the approximation method introduced in \cite{FYW}, the existence and uniqueness are proved for a class of distribution-dependent stochastic functional differential equations (DDSFDEs). Moreover, combining the Harnack and shift-Harnack inequalities for classical stochastic functional differential equations with Girsanov's theorem, Harnack and shift-Harnack inequalities are obtained for the non-linear semigroup $P_t^*$ associated to the functional solution.

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Xing Huang. 2016-12-27. Distribution-Dependent Stochastic Functional Differential Equations. https://arxiv.org/abs/1612.08542

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