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Sur l'intégration stochastique par rapport à une martingale hilbertienne de carré intégrable
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  • Published: 01 February 1989

Sur l'intégration stochastique par rapport à une martingale hilbertienne de carré intégrable

  • Carlo Asperti1 

Probability Theory and Related Fields volume 81, pages 139–158 (1989)Cite this article

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Summary

We give a complete characterization of the operator-valued processes which are integrable, in the sense of [6], with respect to a fixed Hilbertvalued square integrable martingale M. This characterisation allows to complete the theory of stochastic integration with respect to Hilbert-valued martingales. In particular, we give a construction of the process ≪M, N≫ (predictable compensator of M⊗N), as well as a Hilbert-valued version of the Kunita-Watanabe inequality. Finally, we deal with the distributivity of the stochastic integral X·M with respect to the martingale M: this property can be usefully applied to obtain a simple proof of a representation theorem of Gal'tchouk-Métivier.

The results of this article have been announced in Comptes Rendus Note [1].

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Bibliographie

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Authors and Affiliations

  1. Dipartimento di Matematica, Via Buonarroti, 2, I-56100, Pisa, Italy

    Carlo Asperti

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  1. Carlo Asperti
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Asperti, C. Sur l'intégration stochastique par rapport à une martingale hilbertienne de carré intégrable. Probab. Th. Rel. Fields 81, 139–158 (1989). https://doi.org/10.1007/BF00343740

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  • Received: 23 June 1986

  • Revised: 08 August 1988

  • Published: 01 February 1989

  • Issue Date: February 1989

  • DOI: https://doi.org/10.1007/BF00343740

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