%0 Conference Proceedings %T On the Importance of the Levy Area for Studying the Limits of Functions of Converging Stochastic Processes. Application to Homogenization %+ Institut Élie Cartan de Nancy (IECN) %+ Probabilistic numerical methods (OMEGA) %+ Mathematical Institute [Oxford] (MI) %A Lejay, Antoine %A Lyons, Terry, J. %Z Réseau Européen TMR Stochastic Analysis (Project ERBF MRX CT 960075A, grant reference 960075) %F Invité %< avec comité de lecture %B Current Trends in Potential Theory %C Bucarest %Y D. Bakry %Y L. Beznea %Y Gh. Bucur %Y M. Röckner %I The Theta foundation / American Mathematical Society %3 Current Trends in Potential Theory Conference Proceedings, Bucharest, September 2002 and 2003 %V 7 %8 2003 %D 2003 %K rough paths %K homogenization %K approximation of SDEs by ODEs %K Lévy area: convergence of stochastic processes %K p-variation %Z AMS 60J60 (secondary) 35B27, 60F17 %Z Mathematics [math]/Probability [math.PR]Conference papers %X 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. %G English %2 https://inria.hal.science/inria-00092419/document %2 https://inria.hal.science/inria-00092419/file/lejay-lyons.pdf %L inria-00092419 %U https://inria.hal.science/inria-00092419 %~ CNRS %~ INRIA %~ INPL %~ INRIA-SOPHIA %~ IRISA %~ IECN %~ INSMI %~ INRIASO %~ INRIA_TEST %~ TESTALAIN1 %~ UNIV-LORRAINE %~ INRIA2 %~ UR1-MATH-STIC %~ UR1-UFR-ISTIC %~ INRIA-300009 %~ UR1-MATH-NUM %~ INRIA-ROYAUMEUNI