Publications de l'Institut Mathématique, Nouvelle SérieVol. 90(105), pp. 65–84 (2011)
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Publications de l'Institut Mathématique, Nouvelle Série Vol. 90(105), pp. 65–84 (2011) |
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CHAOS EXPANSION METHODS FOR STOCHASTIC DIFFERENTIAL EQUATIONS INVOLVING THE MALLIAVIN DERIVATIVE–PART ITijana Levajkovic and Dora SelesiDepartment of Mathematics and Informatics, Faculty of Traffic and Transport Engineering, University of Belgrade, Serbia; Department of Mathematics and Informatics, Faculty of Science, University of Novi Sad, SerbiaAbstract: 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. 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 Classification (MSC2000): 60H40, 60H10, 60H07, 60G20 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 16 Nov 2011. This page was last modified: 30 Nov 2011.
© 2011 Mathematical Institute of the Serbian Academy of Science and Arts
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