Geodesic
Chaos Expansion Methods for Stochastic Differential Equations Involving the Malliavin Derivative–Part I
Publications de l'Institut Mathématique, _N_S_90 (2011) no. 104, p. 65 .

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

We consider Gaussian, Poissonian, fractional Gaussian and fractional Poissonian white noise spaces, all represented through the corresponding orthogonal basis of the Hilbert space of random variables with finite second moments, given by the Hermite and the Charlier polynomials. There exist unitary mappings between the Gaussian and Poissonian white noise spaces. We investigate the relationship of the Malliavin derivative, the Skorokhod integral, the Ornstein-Uhlenbeck operator and their fractional counterparts on a general white noise space.
Classification : 60H40 60H10 60H07 60G20
Keywords: Gaussian white noise space, Poissonian white noise space, fractional Gaussian white noise space, fractional Poissonian white noise space, series expansion, Malliavin derivative, Skorokhod integral, Ornstein-Uhlenbeck operator 
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     author = {Tijana Levajkovi\'c and Dora Sele\v{s}i},
     title = {Chaos {Expansion} {Methods} for {Stochastic} {Differential} {Equations} {Involving} the {Malliavin} {Derivative{\textendash}Part} {I}},
     journal = {Publications de l'Institut Math\'ematique},
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Tijana Levajković; Dora Seleši. Chaos Expansion Methods for Stochastic Differential Equations Involving the Malliavin Derivative–Part I. Publications de l'Institut Mathématique, _N_S_90 (2011) no. 104, p. 65 . http://geodesic.mathdoc.fr/item/PIM_2011_N_S_90_104_a4/