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

Research output: Contribution to journal › Article › peer-review

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 Itô formula for f(X), where f is of class C²(R) and X admits a generalized bracket [x, X].

Original language	English
Pages (from-to)	81-104
Number of pages	24
Journal	Stochastic Processes and their Applications
Volume	59
Issue number	1
DOIs	https://doi.org/10.1016/0304-4149(95)93237-A
Publication status	Published - 1 Jan 1995
Externally published	Yes

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title = "The generalized covariation process and Ito formula",

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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AB - 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].

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DO - 10.1016/0304-4149(95)93237-A

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JO - Stochastic Processes and their Applications

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The generalized covariation process and Ito formula

Abstract

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