论文标题
稳定过程驱动的多尺度随机动力学系统的平均原理较弱
Weak averaging principle for multiscale stochastic dynamical systems driven by stable processes
论文作者
论文摘要
我们研究了多尺度随机动力学系统家族的平均原理。系统的快速和缓慢组件是由两个独立的稳定lévy噪声驱动的，它们的稳定索引可能不同。同质化索引$ r_0 $的慢组件与稳定的索引$α_1$的快速组件的噪声与$ 0 <r_0 <r_0 <2-2/{α_1} $之间的关系。通过首先研究非局部泊松方程，然后构建合适的校正器，我们可以获得慢速成分弱收敛到Lévy过程，因为比例参数为零。
We study the averaging principle for a family of multiscale stochastic dynamical systems. The fast and slow components of the systems are driven by two independent stable Lévy noises, whose stable indexes may be different. The homogenizing index $r_0$ of slow components has a relation with the stable index $α_1$ of the noise of fast components given by $0<r_0<2-2/{α_1}$. By first studying a nonlocal Poisson equation and then constructing suitable correctors, we obtain that the slow components weakly converge to a Lévy process as the scale parameter goes to zero.
