inria-00092419, version 1
On the Importance of the Levy Area for Studying the Limits of Functions of Converging Stochastic Processes. Application to Homogenization
Antoine Lejay
a, 1, 2Terry J. Lyons 3
Current Trends in Potential Theory 7 (2003)
Résumé : Two concrete examples show us that the convergence of a family of stochastic processes "as controls", i.e. as integrators of SDEs or differential forms, may require more information than simply the limit in the uniform norm of the processes. This may be particularly important when one deals with the homogenization theory. The theory of rough paths is then used to bring some new results about interchanging limits and functionals of stochastic processes.
- a – INRIA
- 1 : Institut Elie Cartan Nancy (IECN)
- CNRS : UMR7502 – INRIA – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine (INPL)
- 2 : OMEGA (INRIA Sophia Antipolis / INRIA Lorraine / IECN)
- CNRS : UMR7502 – INRIA – Université Henri Poincaré - Nancy I – Université Nancy II
- 3 : Mathematical Institute [Oxford] (MI)
- University of Oxford
- Domaine : Mathématiques/Probabilités
- Mots-clés : rough paths – homogenization – approximation of SDEs by ODEs – Lévy area: convergence of stochastic processes – p-variation
- inria-00092419, version 1
- http://hal.inria.fr/inria-00092419
- oai:hal.inria.fr:inria-00092419
- Contributeur : Antoine Lejay
- Soumis le : Dimanche 10 Septembre 2006, 11:03:19
- Dernière modification le : Lundi 11 Septembre 2006, 10:31:57
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