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Proceedings of the American Mathematical Society

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From random walks to rough paths


Authors: Emmanuel Breuillard, Peter Friz and Martin Huesmann
Journal: Proc. Amer. Math. Soc. 137 (2009), 3487-3496
MSC (2000): Primary 60B15
Published electronically: May 20, 2009
MathSciNet review: 2515418
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Abstract: Donsker's invariance principle is shown to hold for random walks in rough path topology. As an application, we obtain Donsker-type weak limit theorems for stochastic integrals and differential equations.


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Additional Information

Emmanuel Breuillard
Affiliation: Laboratoire de Mathematiques, Universite Paris 11, 91405 Orsay, France

Peter Friz
Affiliation: Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Cambridge CB3 0WB, United Kingdom
Email: P.K.Friz@statslab.cam.ac.uk

Martin Huesmann
Affiliation: Mathematisches Institut, Universität Bonn, Endenicher Allee 60, D-53115 Bonn, Germany

DOI: https://doi.org/10.1090/S0002-9939-09-09930-4
Keywords: Donskers's theorem, rough paths
Received by editor(s): October 16, 2008
Published electronically: May 20, 2009
Communicated by: Peter A. Clarkson
Article copyright: © Copyright 2009 American Mathematical Society