| 李钰静1，马 丽1，2*.带奇异系数的McKean-Vlasov随机
微分方程解的存在性[J].海南师范大学学报自科版,2021,34(3):256-268 |
| 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 DifferentialEquations with Singular Coefficients |
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| DOI：10.12051/j.issn.1674-4942.2021.03.002 |
| 中文关键词: 分布依赖的随机微分方程 Zvonkin转换 系数退化 |
| 英文关键词: distribution dependent stochastic differential equations Zvonkin's transformation coefficient degradation |
| 基金项目:国家自然科学基金项目（11861029）；海南省高层次人才项目（120RC589）；海南省研究生创新科研项目
（Hys2020-325） |
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| 中文摘要: |
| 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Hölder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。 |
| 英文摘要: |
| 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,
Hölder 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. |
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