论文标题
在任意时刻，稳定性，独特性和解决方案的解决方案
Stability, uniqueness and existence of solutions to McKean-Vlasov SDEs in arbitrary moments
论文作者
论文摘要
我们推断出具有随机系数和多维的布朗运动作为驱动器的McKean-Vlasov方程的稳定性和唯一性。我们的分析侧重于非lipschitz漂移系数，并包括具有独立感兴趣的随机ITô过程的力矩估计。对于确定性系数，即使漂移未能具有仿射增长，我们也提供独特的强解决方案。我们开发的理论取决于ITô的公式，并导致$ p $ - 第3章，而$ p \ geq 2 $和$α> 0 $的指数稳定性，无论lyapunov是否存在，都具有明显的lyapunov指数。
We deduce stability and pathwise uniqueness for a McKean-Vlasov equation with random coefficients and a multidimensional Brownian motion as driver. Our analysis focuses on a non-Lipschitz drift coefficient and includes moment estimates for random Itô processes that are of independent interest. For deterministic coefficients we provide unique strong solutions, even if the drift fails to be of affine growth. The theory that we develop rests on Itô's formula and leads to $p$-th moment and pathwise $α$-exponential stability for $p\geq 2$ and $α> 0$ with explicit Lyapunov exponents, regardless of whether a Lyapunov function exists.
