论文标题
稳定驱动的McKean-Vlasov SDES的混乱的定量弱传播
Quantitative weak propagation of chaos for stable-driven McKean-Vlasov SDEs
论文作者
论文摘要
我们考虑了一个通用的McKean-Vlasov随机微分方程，该方程是由$ \ Mathbb {r}^d $带有$α\ in（1,2）$的旋转不变的$α$稳定过程驱动的。我们假设扩散系数是身份矩阵，并且漂移是有界的，并且相对于空间和测量变量，从某种意义上说，h {Ö} lder连续连续。这项工作的主要目的是证明与相关的平均场相互作用粒子系统的混乱估计值的新繁殖。我们的研究依赖于与McKean-Vlasov随机微分方程相关的正规化属性和动态，该方程的作用在$ \ Mathcal {p}_β（\ Mathbb {r}^d）上定义的函数上（1，α）$。更准确地说，Semigroup的动力学是由在条$ [0，T] \ times \ Mathcal {p}_β（\ Mathbb {r}^d）$上定义的向后kolmogorov部分微分方程。
We consider a general McKean-Vlasov stochastic differential equation driven by a rotationally invariant $α$-stable process on $\mathbb{R}^d$ with $α\in (1,2)$. We assume that the diffusion coefficient is the identity matrix and that the drift is bounded and H{ö}lder continuous in some precise sense with respect to both space and measure variables. The main goal of this work is to prove new propagation of chaos estimates, at the level of semigroup, for the associated mean-field interacting particle system. Our study relies on the regularizing properties and the dynamics of the semigroup associated with the McKean-Vlasov stochastic differential equation, which acts on functions defined on $\mathcal{P}_β(\mathbb{R}^d)$, the space of probability measures on $\mathbb{R}^d$ having a finite moment of order $β\in (1,α)$. More precisely, the dynamics of the semigroup is described by a backward Kolmogorov partial differential equation defined on the strip $[0,T] \times \mathcal{P}_β(\mathbb{R}^d)$.
