Multiple fractional integral with Hurst parameter less than 1/2

Xavier Bardina; Maria Jolis

doi:https://doi.org/10.1016/j.spa.2005.09.009

Multiple fractional integral with Hurst parameter less than 1/2

Xavier Bardina, Maria Jolis

Department of Mathematics

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

13 Citations (Scopus)

Abstract

We construct a multiple Stratonovich-type integral with respect to the fractional Brownian motion with Hurst parameter H<12. This integral is obtained by a limit of Riemann sums procedure in the Solé and Utzet [Stratonovich integral and trace, Stochastics Stochastics Rep. 29 (2) (1990) 203-220] sense. We also define the suitable traces to obtain the Hu-Meyer formula that gives the Stratonovich integral as a sum of Itô integrals of these traces. Our approach is intrinsic in the sense that we do not make use of the integral representation of the fractional Brownian motion in terms of the ordinary Brownian motion. © 2005 Elsevier B.V. All rights reserved.

Original language	English
Pages (from-to)	463-479
Journal	Stochastic Processes and their Applications
Volume	116
DOIs	https://doi.org/10.1016/j.spa.2005.09.009
Publication status	Published - 1 Mar 2006

Keywords

Fractional Brownian motion
Hu-Meyer formula
Itô-type multiple integral
Stratonovich multiple integral

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title = "Multiple fractional integral with Hurst parameter less than 1/2",

abstract = "We construct a multiple Stratonovich-type integral with respect to the fractional Brownian motion with Hurst parameter H<12. This integral is obtained by a limit of Riemann sums procedure in the Sol{\'e} and Utzet [Stratonovich integral and trace, Stochastics Stochastics Rep. 29 (2) (1990) 203-220] sense. We also define the suitable traces to obtain the Hu-Meyer formula that gives the Stratonovich integral as a sum of It{\^o} integrals of these traces. Our approach is intrinsic in the sense that we do not make use of the integral representation of the fractional Brownian motion in terms of the ordinary Brownian motion. {\textcopyright} 2005 Elsevier B.V. All rights reserved.",

keywords = "Fractional Brownian motion, Hu-Meyer formula, It{\^o}-type multiple integral, Stratonovich multiple integral",

author = "Xavier Bardina and Maria Jolis",

year = "2006",

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TY - JOUR

T1 - Multiple fractional integral with Hurst parameter less than 1/2

AU - Bardina, Xavier

AU - Jolis, Maria

PY - 2006/3/1

Y1 - 2006/3/1

N2 - We construct a multiple Stratonovich-type integral with respect to the fractional Brownian motion with Hurst parameter H<12. This integral is obtained by a limit of Riemann sums procedure in the Solé and Utzet [Stratonovich integral and trace, Stochastics Stochastics Rep. 29 (2) (1990) 203-220] sense. We also define the suitable traces to obtain the Hu-Meyer formula that gives the Stratonovich integral as a sum of Itô integrals of these traces. Our approach is intrinsic in the sense that we do not make use of the integral representation of the fractional Brownian motion in terms of the ordinary Brownian motion. © 2005 Elsevier B.V. All rights reserved.

AB - We construct a multiple Stratonovich-type integral with respect to the fractional Brownian motion with Hurst parameter H<12. This integral is obtained by a limit of Riemann sums procedure in the Solé and Utzet [Stratonovich integral and trace, Stochastics Stochastics Rep. 29 (2) (1990) 203-220] sense. We also define the suitable traces to obtain the Hu-Meyer formula that gives the Stratonovich integral as a sum of Itô integrals of these traces. Our approach is intrinsic in the sense that we do not make use of the integral representation of the fractional Brownian motion in terms of the ordinary Brownian motion. © 2005 Elsevier B.V. All rights reserved.

KW - Fractional Brownian motion

KW - Hu-Meyer formula

KW - Itô-type multiple integral

KW - Stratonovich multiple integral

U2 - https://doi.org/10.1016/j.spa.2005.09.009

DO - https://doi.org/10.1016/j.spa.2005.09.009

M3 - Article

VL - 116

SP - 463

EP - 479

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

SN - 0304-4149

ER -