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Title: An extension of Itô's formula for anticipating processes
Author: Alòs, Elisa
Nualart, David, 1951-
Keywords: Integrals estocàstiques
Càlcul de Malliavin
Universitat de Barcelona. Institut de Matemàtica
Issue Date: 1996
Publisher: Universitat de Barcelona
Series/Report no: Mathematics Preprint Series; 215
Abstract: In this paper we introduce a class of square integrable processes, denoted by LF, defined in the canonical probability space of the Brownian motion, which contains both the adapted processes and the processes in the Sobolev space L2,2. The processes in the class LF satisfy that for any time t, they are twice weakly differentiable in the sense of the stochastic calculus of variations in points (r, s) such that r ∨ s ≥ t. On the other hand, processes belonging to the class LF are Skorohod integrable, and the indefinite Skorohod integral has properties similar to those of the Ito integral. In particular we prove a change-of-variable formula that extends the classical Itô formula. Those results are generalization of similar properties proved by Nualart and Pardoux(7) for processes in L2,2.
Note: Preprint enviat per a la seva publicació en una revista científica: Journal of Theoretical Probability, (1998), volume 11, pages 493–514. []
Note: Reproducció digital del document original en paper [CRAI Biblioteca de Matemàtiques i Informàtica - Dipòsit Departament CAIXA 37.10]
Appears in Collections:Preprints de Matemàtiques - Mathematics Preprint Series

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