论文标题
带有自动稳定术语和超级线性漂移的麦基恩 - 弗拉索夫方程式反射的大偏差和出口
Large Deviations and Exit-times for reflected McKean-Vlasov equations with self-stabilizing terms and superlinear drifts
论文作者
论文摘要
我们研究了具有自动化系数的一类反射的McKean-Vlasov扩散。这包括无法满足古典Wasserstein Lipschitz条件的系数。此外，该过程被限制在边界上的本地时间（不一定是有限的）凸域。这些方程包括反射的自动扩散的子类，通过具有稳定潜力的解决方案定律的卷积向其平均值漂移。 首先，我们为此类别建立了存在和独特性结果，并解决了混乱的传播。我们使用广泛的系数，包括在空间和测量变量中局部Lipschitz的漂移项。但是，我们不依赖域或系数的界限来解释这些非线性，而是使用自稳定的属性。 我们证明了弗里德林 - 温泽尔型的大偏差原理，以及从反射域内部包含的子域中退出子域的眼睛 - kramer定律。
We study a class of reflected McKean-Vlasov diffusions over a convex domain with self-stabilizing coefficients. This includes coefficients that do not satisfy the classical Wasserstein Lipschitz condition. Further, the process is constrained to a (not necessarily bounded) convex domain by a local time on the boundary. These equations include the subclass of reflected self-stabilizing diffusions that drift towards their mean via a convolution of the solution law with a stabilizing potential. Firstly, we establish existence and uniqueness results for this class and address the propagation of chaos. We work with a broad class of coefficients, including drift terms that are locally Lipschitz in spatial and measure variables. However, we do not rely on the boundedness of the domain or the coefficients to account for these non-linearities and instead use the self-stabilizing properties. We prove a Freidlin-Wentzell type Large Deviations Principle and an Eyring-Kramer's law for the exit-time from subdomains contained in the interior of the reflecting domain.
