Non-degeneracy of Wiener functionals arising from rough differential equations

Thomas Cass; Peter Friz; Nicolas Victoir

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arXiv · 0707.0154

Non-degeneracy of Wiener functionals arising from rough differential equations

Thomas Cass·Peter Friz·Nicolas Victoir

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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 solution to (possibly stochastic) differential equations. We combine arguments of both theories and discuss 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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BibTeX RIS

Thomas Cass, Peter Friz, Nicolas Victoir. 2007-11-12. Non-degeneracy of Wiener functionals arising from rough differential equations. https://arxiv.org/abs/0707.0154

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