紧叶上重尾Lévy扩散的强平均
Strong averaging along foliated Lévy diffusions with heavy tails on compact leaves
摘要：
本文证明了由不连续重尾Lévy噪声驱动的扩散的强平均原理，它在受小的横向随机扰动的叶状流形的紧致水平叶上是不变的。我们延长这样的扩散指数矩和有界的，确定性扰动的扩散与多项式矩的顺序$p\geq 2$，扰动确定性和随机积分与无界系数和多项式矩的结果。主要参数依赖于相应的规范马库斯方程的每个单独的跳跃增量的动力系统的结果。详细地给出了单位圆上受平面Lévy-Ornstein-Uhlenbeck过程扰动的Lévy旋转的例子。
英文摘要：
This article shows a strong averaging principle for diffusions driven by discontinuous heavy-tailed Lévy noise, which are invariant on the compact horizontal leaves of a foliated manifold subject to small transversal random perturbations. We extend a result for such diffusions with exponential moments and bounded, deterministic perturbations to diffusions with polynomial moments of order $p\geq 2$, perturbed by deterministic and stochastic integrals with unbounded coefficients and polynomial moments. The main argument relies on a result of the dynamical system for each individual jump increments of the corresponding canonical Marcus equation. The example of Lévy rotations on the unit circle subject to perturbations by a planar Lévy-Ornstein-Uhlenbeck process is carried out in detail.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
