Distribution-Dependent Stochastic Functional Differential Equations

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 $P_t^{\ast }$ associated to the functional solution.

We have submitted a new version which is arXiv:1709.00556

References in corpus (4)

• Harnack Inequalities for Functional SDEs with Multiplicative Noise and Applications
• Shift Harnack Inequality and Integration by Part Formula for Semilinear SPDE
• Distribution-Dependent SDEs for Landau Type Equations
• Stochastic Hamiltonian flows with singular coefficients