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Electronic Journal of Probability 7, 18 (2003) 1-18

Versions disponibles

v1 (15-09-2006)

v2 (13-10-2006)

On the convergence of stochastic integrals driven by processes converging on account of a homogenization property

Antoine Lejay 1, 2

(2003)

We study the limit of functionals of stochastic processes for which an homogenization result holds. All these functionals involve stochastic integrals. Among them, we consider more particularly the Lévy area and those giving the solutions of some SDEs. The main question is to know whether or not the limit of the stochastic integrals is equal to the stochastic integral of the limit of each of its terms. In fact, the answer may be negative, especially in presence of a highly oscillating first-order differential term. This provides us some counterexamples to the theory of good sequence of semimartingales.

1 :	Institut Elie Cartan Nancy (IECN)
	CNRS : UMR7502 – INRIA – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine
2 :	OMEGA (INRIA Sophia Antipolis / INRIA Lorraine / IECN)
	CNRS : UMR7502 – INRIA – Université Henri Poincaré - Nancy I – Université Nancy II

Domaine

:

Mathématiques/Probabilités

Mots-clés : homogenization – stochastic differential equations – good sequence of semimartingales – conditions UT and UCV – Levy area

inria-00093190, version 2

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Contributeur : Antoine Lejay <>

Soumis le : Vendredi 13 Octobre 2006, 14:13:05

Dernière modification le : Vendredi 13 Octobre 2006, 14:54:14