Strong averaging along foliated Lévy diffusions with heavy tails on compact leaves

Michael A. Högele; Paulo-Henrique da Costa

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arXiv · 1507.07530

Strong averaging along foliated Lévy diffusions with heavy tails on compact leaves

Michael A. Högele·Paulo-Henrique da Costa

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Abstract

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.

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Michael A. Högele, Paulo-Henrique da Costa. 2016-08-26. Strong averaging along foliated Lévy diffusions with heavy tails on compact leaves. https://arxiv.org/abs/1507.07530

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