Distribution-Dependent Stochastic Functional Differential Equations

2016/12/27 by Xing Huang, Huang, Xing
Economics, Econometrics and Finance · Mathematics · #Advanced Harmonic Analysis Research #FOS: Mathematics #Nonlinear Differential Equations Analysis #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1612.08542

openalex publication_date 2016/12/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

By the approximation method introduced in \citeFYW, 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.

Citations

• Integration by Parts Formula and Applications for SDEs with Lévy Noise
• Stochastic Hamiltonian flows with singular coefficients

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