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Non-Degeneracy of Wiener Functionals Arising from Rough Differential Equations

Thomas Cass, Peter Friz and Nicolas Victoir
Transactions of the American Mathematical Society
Vol. 361, No. 6 (Jun., 2009), pp. 3359-3371
Stable URL: http://www.jstor.org/stable/40302901
Page Count: 13
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Non-Degeneracy of Wiener Functionals Arising from Rough Differential Equations
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Abstract

Malliavin Calculus is about Sobolev-type regularity of functionals on Wiener space, the main example being the Ito 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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