The generalized covariation process and Ito formula

Francesco Russo; Pierre Vallois

doi:10.1016/0304-4149(95)93237-A

The generalized covariation process and Ito formula

Francesco Russo
, Pierre Vallois

Institut Galilée
Bielefeld University
Nancy Université

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

If X and Y are two general stochastic processess, we define a covariation process [X, Y] with the help of a limit procedure. When the processes are semimartingales, [X, Y] is their classical bracket. We calculate covariation for some important examples arising from anticipating stochastic calculus and we establish a Itô formula for f(X), where f is of class C²(R) and X admits a generalized bracket [x, X].

langue originale	Anglais
Pages (de - à)	81-104
Nombre de pages	24
journal	Stochastic Processes and their Applications
Volume	59
Numéro de publication	1
Les DOIs	https://doi.org/10.1016/0304-4149(95)93237-A
état	Publié - 1 janv. 1995
Modification externe	Oui

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10.1016/0304-4149(95)93237-A

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abstract = "If X and Y are two general stochastic processess, we define a covariation process [X, Y] with the help of a limit procedure. When the processes are semimartingales, [X, Y] is their classical bracket. We calculate covariation for some important examples arising from anticipating stochastic calculus and we establish a It{\^o} formula for f(X), where f is of class C2(R) and X admits a generalized bracket [x, X].",

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The generalized covariation process and Ito formula

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