The covariation for Banach space valued processes and applications

Cristina Di Girolami (), Giorgio Fabbri and Francesco Russo ()
Additional contact information
Cristina Di Girolami: Laboratoire Manceau de Mathématiques, Université du Maine, http://lmm.univ-lemans.fr/fr/index.html
Francesco Russo: ENSTA ParisTech, Unité de Mathématiques appliquées, https://uma.ensta-paris.fr/

No 13-01, Documents de recherche from Centre d'Études des Politiques Économiques (EPEE), Université d'Evry Val d'Essonne

Abstract: This article focuses on a new concept of quadratic variation for processes taking values in a Banach space B and a corresponding covariation. This is more general than the classical one of Métivier and Pellaumail. Those notions are associated with some subspace ? of the dual of the projective tensor product of B with itself. We also introduce the notion of a convolution type process, which is a natural generalization of the Itô process and the concept of ¯V0-semimartingale, which is a natural extension of the classical notion of semimartingale. The framework is the stochastic calculus via regularization in Banach spaces. Two main applications are mentioned: one related to Clark-Ocone formula for finite quadratic variation processes; the second one concerns the probabilistic representation of a Hilbert valued partial differential equation of Kolmogorov type. 2010 Math Subject Classification: 60G22, 60H05, 60H07, 60H15, 60H30, 26E20, 35K90 46G05

Keywords: Calculus via regularization; Infinite dimensional analysis; Tensor analysis; Clark-Ocone formula; Dirichlet processes; Itô formula; Quadratic variation; Stochastic partial differential equations; Kolmogorov equation (search for similar items in EconPapers)
Pages: 45 pages
Date: 2013-01
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Citations: View citations in EconPapers (1)

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Journal Article: The covariation for Banach space valued processes and applications (2014)
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