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Non-degeneracy of Wiener functionals arising from rough differential equations


Authors: Thomas Cass, Peter Friz and Nicolas Victoir
Journal: Trans. Amer. Math. Soc. 361 (2009), 3359-3371
MSC (2000): Primary 60G15, 60H07, 60H10, 60K99
Published electronically: January 28, 2009
MathSciNet review: 2485431
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Abstract | References | Similar Articles | Additional Information

Abstract: Malliavin Calculus is about Sobolev-type regularity of functionals on Wiener space, the main example being the Itô map obtained by solving stochastic differential equations. Rough path analysis is about strong regularity of the solution to (possibly stochastic) differential equations. We combine arguments of both theories and discuss the existence of a density for solutions to stochastic differential equations driven by a general class of non-degenerate Gaussian processes, including processes with sample path regularity worse than Brownian motion.


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Additional Information

Thomas Cass
Affiliation: Department of Pure Mathematics and Statistics, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WB, United Kingdom
Address at time of publication: Mathematical Institute, University of Oxford, 24-29 St. Giles’, Oxford, OX1 3LB, United Kingdom

Peter Friz
Affiliation: Department of Pure Mathematics and Statistics, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WB, United Kingdom

DOI: http://dx.doi.org/10.1090/S0002-9947-09-04677-7
Keywords: Malliavin Calculus, rough paths analysis
Received by editor(s): May 11, 2007
Received by editor(s) in revised form: November 7, 2007
Published electronically: January 28, 2009
Article copyright: © Copyright 2009 American Mathematical Society