| 王 如1， 马 丽1，2*.带跳的McKean-Vlasov随机微分方程解的
存在唯一性[J].海南师范大学学报自科版,2020,33(4):365-373 |
| 带跳的McKean-Vlasov随机微分方程解的
存在唯一性 |
| The Existence and Uniqueness of Solutions of McKean - VlasovStochastic Differential Equations with Jumps |
| |
| DOI：10.12051/j.issn.1674-4942.2020.04.001 |
| 中文关键词: 跳测度 Lyapunov条件 McKean-Vlasov随机微分方程 弱解的存在唯一性 |
| 英文关键词: jump measure Lyapunov condition McKean-Vlasov stochastic differential equations existence and
uniqueness of weak solutions |
| 基金项目:海南省自然科学基金项目（118MS040）；海南省高等学校科学研究项目（Hnky2018ZD-6）；国家自然科学基金
项目（11861029） |
|
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| 中文摘要: |
| 文章讨论了带跳的McKean-Vlasov随机微分方程解的存在唯一性。在系数满足连续
性及局部有界性的条件下，用局部化的方法，结合Itô公式、弱收敛、Skorohod's表示定理等工具，得
到了弱解的存在唯一性。本研究不要求扩散项系数的非退化性，允许方程中含有跳测度，从而拓
展了McKean-Vlasov随机微分方程解的存在唯一性方面的结果。 |
| 英文摘要: |
| In this paper, the existence and uniqueness of solutions of McKean-Vlasov stochastic differential equations
with jumps was considered. With the condition that the coefficients are continuous and locally bounded, the existence and
uniqueness of the weak solutions were obtained by using the method of localization and combining Itô formula, weak conver⁃
gence, Skorohod's representation theorem and other tools. The nondegeneracy of diffusion coefficients was not required,
and jump measures were allowed in the equations, thus the results of existence and uniqueness of the solutions of distribu⁃
tion-dependent stochastic differential equations were extended. |
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