Wiener integrals, Malliavin calculus and covariance measure structure

Ida Kruk; Francesco Russo; Ciprian A. Tudor

doi:10.1016/j.jfa.2007.03.031

Wiener integrals, Malliavin calculus and covariance measure structure

Ida Kruk
, Francesco Russo
, Ciprian A. Tudor

Institut Galilée
Paris School of Economics

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

58 Citations (Scopus)

Abstract

We introduce the notion of covariance measure structure for square integrable stochastic processes. We define Wiener integral, we develop a suitable formalism for stochastic calculus of variations and we make Gaussian assumptions only when necessary. Our main examples are finite quadratic variation processes with stationary increments and the bifractional Brownian motion.

Original language	English
Pages (from-to)	92-142
Number of pages	51
Journal	Journal of Functional Analysis
Volume	249
Issue number	1
DOIs	https://doi.org/10.1016/j.jfa.2007.03.031
Publication status	Published - 1 Aug 2007
Externally published	Yes

Keywords

Bifractional Brownian motion
Covariance measure structure
Malliavin calculus
Skorohod integral
Square integrable processes

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10.1016/j.jfa.2007.03.031

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title = "Wiener integrals, Malliavin calculus and covariance measure structure",

abstract = "We introduce the notion of covariance measure structure for square integrable stochastic processes. We define Wiener integral, we develop a suitable formalism for stochastic calculus of variations and we make Gaussian assumptions only when necessary. Our main examples are finite quadratic variation processes with stationary increments and the bifractional Brownian motion.",

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AU - Russo, Francesco

AU - Tudor, Ciprian A.

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KW - Bifractional Brownian motion

KW - Covariance measure structure

KW - Malliavin calculus

KW - Skorohod integral

KW - Square integrable processes

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DO - 10.1016/j.jfa.2007.03.031

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JO - Journal of Functional Analysis

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Wiener integrals, Malliavin calculus and covariance measure structure

Abstract

Keywords

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