The covariation for Banach space valued processes and applications
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
|Date of creation:||Jan 2013|
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- 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.
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- Errami, Mohammed & Russo, Francesco, 2003. "n-covariation, generalized Dirichlet processes and calculus with respect to finite cubic variation processes," Stochastic Processes and their Applications, Elsevier, vol. 104(2), pages 259-299, April.
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- 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.
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