论文标题
二次潜能中动力学不均匀随机系统的缩放极限
Scaling limit of a kinetic inhomogeneous stochastic system in the quadratic potential
论文作者
论文摘要
我们认为粒子在二次潜力中进化，并受到时间均匀的摩擦力和随机力的影响。这对夫妇的速度和位置是解决随机微分方程的方法根据噪声的摩擦力与稳定性指数$α$之间的平衡进行缩放。
We consider a particle evolving in the quadratic potential and subject to a time-inhomogeneous frictional force and to a random force. The couple of its velocity and position is solution to a stochastic differential equation driven by an $α$-stable L{é}vy process with $α\in (1,2]$ and the frictional force is of the form $t^{-β}\text{sgn}(v)|v|^γ$. We identify three regimes for the behavior in long-time of the couple velocity-position with a suitable rescaling, depending on the balance between the frictional force and the index of stability $α$ of the noise.
