论文标题
关于多维McKean-Vlasov方程的路径唯一性
On pathwise uniqueness for multidimensional McKean--Vlasov equations
论文作者
论文摘要
多维随机McKean-vlasov方程的途径唯一性是在中等规律性条件下在漂移和扩散系数的中等规则条件下建立的。漂移和扩散都取决于溶液的边际度量。对于路径的唯一性，假定漂移在状态变量中是二合一的连续性，而扩散必须是Lipschitz，时间连续，并且均匀地不化。该设置是经典的McKean-Vlasov，即方程的系数表示为在过程的边际分布上的积分。
Pathwise uniqueness for multi-dimensional stochastic McKean--Vlasov equation is established under moderate regularity conditions on the drift and diffusion coefficients. Both drift and diffusion depend on the marginal measure of the solution. For pathwise uniqueness, the drift is assumed to be Dini-continuous in the state variable, while the diffusion must be Lipschitz, continuous in time and uniformly nondegenerate. The setting is classical McKean--Vlasov, that is, coefficients of the equation are represented as integrals over the marginal distributions of the process.
