On the Importance of the Levy Area for Studying the Limits of Functions of Converging Stochastic Processes. Application to Homogenization

Antoine Lejay 1, 2 Terry Lyons 3
2 OMEGA - Probabilistic numerical methods
CRISAM - Inria Sophia Antipolis - Méditerranée , UHP - Université Henri Poincaré - Nancy 1, Université Nancy 2, CNRS - Centre National de la Recherche Scientifique : UMR7502
Abstract : 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.
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Antoine Lejay, Terry Lyons. On the Importance of the Levy Area for Studying the Limits of Functions of Converging Stochastic Processes. Application to Homogenization. Current Trends in Potential Theory, 2003, Bucarest. ⟨inria-00092419⟩

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