The covariation for Banach space valued processes and applications
AbstractThis 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
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Centre d'Études des Politiques Économiques (EPEE), Université d'Evry Val d'Essonne in its series Documents de recherche with number 13-01.
Length: 45 pages
Date of creation: Jan 2013
Date of revision:
Calculus via regularization; Infinite dimensional analysis; Tensor analysis; Clark-Ocone formula; Dirichlet processes; Itô formula; Quadratic variation; Stochastic partial differential equations; Kolmogorov equation;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-04-13 (All new papers)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Gozzi, Fausto & Russo, Francesco, 2006. "Weak Dirichlet processes with a stochastic control perspective," Stochastic Processes and their Applications, Elsevier, vol. 116(11), pages 1563-1583, November.
- Giorgio FABBRI & Francesco RUSSO, 2012. "Infinite dimensional weak Dirichlet processes, stochastic PDEs and optimal control," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2012017, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
- Christian Bender & Tommi Sottinen & Esko Valkeila, 2008. "Pricing by hedging and no-arbitrage beyond semimartingales," Finance and Stochastics, Springer, vol. 12(4), pages 441-468, October.
- Russo, Francesco & Tudor, Ciprian A., 2006. "On bifractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 116(5), pages 830-856, May.
- Gozzi, Fausto & Russo, Francesco, 2006. "Verification theorems for stochastic optimal control problems via a time dependent Fukushima-Dirichlet decomposition," Stochastic Processes and their Applications, Elsevier, vol. 116(11), pages 1530-1562, November.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Samuel Nosel).
If references are entirely missing, you can add them using this form.