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(Referência obtida automaticamente do Web of Science, por meio da informação sobre o financiamento pela FAPESP e o número do processo correspondente, incluída na publicação pelos autores.)

Averaging along foliated Levy diffusions

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Autor(es):
Hoegele, Michael [1] ; Ruffino, Paulo [2]
Número total de Autores: 2
Afiliação do(s) autor(es):
[1] Univ Potsdam, Math Inst, Potsdam - Germany
[2] Univ Estadual Campinas, IMECC, BR-13081970 Campinas, SP - Brazil
Número total de Afiliações: 2
Tipo de documento: Artigo Científico
Fonte: NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS; v. 112, p. 1-14, JAN 2015.
Citações Web of Science: 5
Resumo

This article studies the dynamics of the strong solution of a SDE driven by a discontinuous Levy process taking values in a smooth foliated manifold with compact leaves. It is assumed that it is foliated in the sense that its trajectories stay on the leaf of their initial value for all times almost surely. Under a generic ergodicity assumption for each leaf, we determine the effective behaviour of the system subject to a small smooth perturbation of order epsilon > 0, which acts transversal to the leaves. The main result states that, on average, the transversal component of the perturbed SDE converges uniformly to the solution of a deterministic ODE as e tends to zero. This transversal ODE is generated by the average of the perturbing vector field with respect to the invariant measures of the unperturbed system and varies with the transversal height of the leaves. We give upper bounds for the rates of convergence and illustrate these results for the random rotations on the circle. This article complements the results by Gonzales and Ruffino for SDEs of Stratonovich type to general Levy driven SDEs of Marcus type. (C) 2014 Elsevier Ltd. All rights reserved. (AU)

Processo FAPESP: 11/50151-0 - Fenômenos dinâmicos em redes complexas: fundamentos e aplicações
Beneficiário:Elbert Einstein Nehrer Macau
Linha de fomento: Auxílio à Pesquisa - Temático
Processo FAPESP: 12/03992-1 - Dinâmica e geometria de fluxos estocásticos
Beneficiário:Paulo Regis Caron Ruffino
Linha de fomento: Bolsas no Exterior - Pesquisa