Strong Averaging Along Foliated Lévy Diffusions with Heavy Tails on Compact Leaves
| Autor: | Michael Högele, Paulo Henrique da Costa |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Polynomial
Dynamical systems theory 010102 general mathematics Mathematical analysis Dynamical system 01 natural sciences Potential theory Exponential function 010104 statistics & probability Unit circle Mathematics::Probability Bounded function 0101 mathematics Invariant (mathematics) Analysis Mathematics |
| Zdroj: | Potential Analysis. 47:277-311 |
| ISSN: | 1572-929X 0926-2601 |
| DOI: | 10.1007/s11118-017-9615-0 |
| Popis: | This article shows a strong averaging principle for diffusions driven by discontinuous heavy-tailed Levy 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 Levy rotations on the unit circle subject to perturbations by a planar Levy-Ornstein-Uhlenbeck process is carried out in detail. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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