论文标题
具有单数相互作用的McKean-Vlasov方程的存在和独特性
Existence and Uniqueness for McKean-Vlasov equations with singular interactions
论文作者
论文摘要
我们调查了以下麦基恩 - vlasov方程在$ \ mathbb {r}^d $：\ [\ mathrm {d} x_t =σ（t，x_t，x_t，μ_{x_t}）\ mathrm {d} \]其中$μ_{x_t} $是$ x_t $的定律。当$σ$满足某些非分类和连续性假设时，解决方案的存在，并且当$ b $符合某些集成性条件时，并且（广义）总变化距离中的连续性要求。此外，在Lipschitz类型的其他连续性假设下建立了唯一性。
We investigate the well-posedness of following McKean-Vlasov equation in $\mathbb{R}^d$: \[ \mathrm{d} X_t=σ(t,X_t, μ_{X_t})\mathrm{d} W_t+b(t, X_t, μ_{X_t}) \mathrm{d} t, \] where $μ_{X_t}$ is the law of $X_t$. The existence of solutions is demonstrated when $σ$ satisfies certain non-degeneracy and continuity assumptions, and when $b$ meets some integrability conditions, and continuity requirements in the (generalized) total variation distance. Furthermore, uniqueness is established under additional continuity assumptions of a Lipschitz type.
