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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
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/40302901
Page Count: 13
You can always find the topics here!Topics: Differential equations, Brownian motion, Covariance, Mathematical integrals, Signals, Calculus, Vector fields, Iterated integrals, Abstract spaces
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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.
Transactions of the American Mathematical Society © 2009 American Mathematical Society