Strong Averaging Along Foliated Lévy Diffusions with Heavy Tails on Compact Leaves

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 momen...

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Bibliographic Details
Published in:Potential analysis 2017-10, Vol.47 (3), p.277-311
Main Authors: Högele, Michael A., da Costa, Paulo Henrique
Format: Article
Language:English
Subjects:
Functional Analysis
Geometry
Mathematics
Mathematics and Statistics
Ornstein-Uhlenbeck process
Polynomials
Potential Theory
Probability Theory and Stochastic Processes
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Summary: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 ≥ 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.
ISSN:0926-2601
1572-929X
DOI:10.1007/s11118-017-9615-0