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1. Non-degeneracy of Wiener functionals arising from rough differential equations.

Author

Thomas Cass, Peter Friz, and Nicolas Victoir

Subjects
*STOCHASTIC differential equations, *CONTINUOUS functions, *FUNCTIONALS, *MALLIAVIN calculus, *MATHEMATICAL mappings, *PATH analysis (Statistics)
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. [ABSTRACT FROM AUTHOR]

Published
2008

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