# The covariation for Banach space valued processes and applications.

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 $\chi$ 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 $\bar \nu_0$-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.
keyword :
Type de document :
Article dans une revue
Metrika, Springer Verlag, 2014, 77 (1), pp.51-104. 〈https://link.springer.com/article/10.1007/s00184-013-0472-6〉
Domaine :

https://hal.inria.fr/hal-00780430
Contributeur : Francesco Russo <>
Soumis le : jeudi 1 août 2013 - 20:22:52
Dernière modification le : lundi 20 novembre 2017 - 15:08:53
Document(s) archivé(s) le : samedi 2 novembre 2013 - 04:12:45

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• HAL Id : hal-00780430, version 2
• ARXIV : 1301.5715

### Citation

Cristina Di Girolami, Giorgio Fabbri, Francesco Russo. The covariation for Banach space valued processes and applications.. Metrika, Springer Verlag, 2014, 77 (1), pp.51-104. 〈https://link.springer.com/article/10.1007/s00184-013-0472-6〉. 〈hal-00780430v2〉

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