带奇异系数的McKean-Vlasov随机微分方程解的存在性

Existence of Solutions for McKean Vlasov Stochastic Differential Equations with Singular Coefficients

本文主要研究分布依赖的随机微分方程弱解的存在性问题。利用Zvonkin转换、Krylov估计、Prokhorov定理、Skorokhod表示定理和H?lder不等式等工具,在扩散系数满足弱连续的条件下得到该随机微分方程弱解的存在性,同时研究了二阶抛物偏微分方程在系数几乎处处有界、退化和一致连续的条件下解的正则性。

In this paper, we studied the existence of solutions for distribution dependent stochastic differential equation.By means of Zvonkin’s transformation, Krylov’s estimation, Prokhorov’s theorem, Skorokhod’s representation theorem,H?lder inequality and other tools, the existence of weak solutions for the stochastic differential equation was obtained under the condition that the diffusion coefficient satisfies weak continuity. At the same time, we studied the regularity of solutions of second order parabolic partial differential equations under the condition that the coefficients are almost everywhere bounded, degenerate and uniformly continuous.