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Your search keyword '"Privault, Nicolas"' showing total 2 results
Start Over Author "Privault, Nicolas" Search Limiters Peer Reviewed Topic malliavin calculus Publication Year Range Last 50 years Publication Type Academic Journals Journal infinite dimensional analysis, quantum probability & related topics
2 results on '"Privault, Nicolas"'

1. De Rham-Hodge decomposition and vanishing of harmonic forms by derivation operators on the Poisson space.

Author

Privault, Nicolas

Subjects
*MATHEMATICAL decomposition, *HARMONIC analysis (Mathematics), *POISSON algebras, *HARMONIC spaces (Mathematics), *COVARIANT canonical quantization
Abstract

We construct differential forms of all orders and a covariant derivative together with its adjoint on the probability space of a standard Poisson process, using derivation operators. In this framewok we derive a de Rham-Hodge-Kodaira decomposition as well as Weitzenböck and Clark-Ocone formulas for random differential forms. As in the Wiener space setting, this construction provides two distinct approaches to the vanishing of harmonic differential forms. [ABSTRACT FROM AUTHOR]

Published
2016
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2. RANDOM HERMITE POLYNOMIALS AND GIRSANOV IDENTITIES ON THE WIENER SPACE.

Author

PRIVAULT, NICOLAS and Franz, U.

Subjects
*HERMITE polynomials, *RANDOM walks, *COMBINATORIAL identities, *WIENER integrals, *MATHEMATICAL proofs, *MATHEMATICAL analysis
Abstract

In this paper, we derive a formula for the expectation of random Hermite polynomials in Skorohod integrals, extending classical results in the adapted case. As an application we recover, under simple conditions and with short proofs, the anticipative Girsanov identity and quasi-invariance results obtained in Ref. 6 for quasi-nilpotent shifts on the Wiener space. [ABSTRACT FROM AUTHOR]

Published
2010
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