## Non-degeneracy of Wiener functionals arising from rough differential equations

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- by Thomas Cass, Peter Friz and Nicolas Victoir PDF
- Trans. Amer. Math. Soc.
**361**(2009), 3359-3371 Request permission

## 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.## References

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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
- MR Author ID: 656436
- Received by editor(s): May 11, 2007
- Received by editor(s) in revised form: November 7, 2007
- Published electronically: January 28, 2009
- © Copyright 2009 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**361**(2009), 3359-3371 - MSC (2000): Primary 60G15, 60H07, 60H10, 60K99
- DOI: https://doi.org/10.1090/S0002-9947-09-04677-7
- MathSciNet review: 2485431