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

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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 \(p\geqslant 2\), 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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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad de los Andes, Bogotá, Colombia

    Michael A. Högele

  2. Departamento de Matemática, Universidade de Brasília, Brasília, Brazil

    Paulo Henrique da Costa

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  1. Michael A. Högele
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  2. Paulo Henrique da Costa
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Correspondence to Michael A. Högele.

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Högele, M.A., da Costa, P.H. Strong Averaging Along Foliated Lévy Diffusions with Heavy Tails on Compact Leaves. Potential Anal 47, 277–311 (2017). https://doi.org/10.1007/s11118-017-9615-0

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  • DOI: https://doi.org/10.1007/s11118-017-9615-0

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