论文标题
Kramers的类型定律，用于两个自动扩散及其粒子近似的第一次碰撞时间
A Kramers' type law for the first collision-time of two self-stabilizing diffusions and of their particle approximations
论文作者
论文摘要
本工作研究了与一对自动稳定扩散及其相关粒子近似相关的第一次碰撞时间和第一次碰撞的渐近行为。这些渐近性在一个特殊的框架中被考虑，在一个特殊的框架中，由于驱动每一次扩散的布朗动作的综合作用以及自动稳定的内核的作用，散射在双孔景观中演变出来。随着布朗效应的消失，我们表明第一次碰撞时间以明确的指数速率增长，并且相关的碰撞位置持续存在在太空的特殊点。这些结果主要是通过将扩散过程的碰撞现象与随机扰动动力学系统的退出问题联系起来，并利用Freidlin-Wentzell的LDP方法来解决这些退出时间问题，从而获得了这些结果。重要的是，我们考虑两种独特的情况：一维情况（可以直接研究真实的碰撞）和一般的多维案例（需要扩大碰撞）。
The present work investigates the asymptotic behaviors, at the zero-noise limit, of the first collision-time and first collision-location related to a pair of self-stabilizing diffusions and of their related particle approximations. These asymptotic are considered in a peculiar framework where diffusions evolve in a double-wells landscape and where collisions manifest due to the combined action of the Brownian motions driving each diffusion and the action of a self-stabilizing kernel. As the Brownian effects vanish, we show that first collision-times grow at an explicit exponential rate and that the related collision-locations persist at a special point in space. These results are mainly obtained by linking collision phenomena for diffusion processes with exit-time problems of random perturbed dynamical systems, and by exploiting Freidlin-Wentzell's LDP approach to solve these exit-time problems. Importantly, we consider two distinctive situations: the one-dimensional case (where true collisions can be directly studied) and the general multidimensional case (where collisions are required to be enlarged).
