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May 2011 A construction of the rough path above fractional Brownian motion using Volterra’s representation
David Nualart, Samy Tindel
Ann. Probab. 39(3): 1061-1096 (May 2011). DOI: 10.1214/10-AOP578

Abstract

This note is devoted to construct a rough path above a multidimensional fractional Brownian motion B with any Hurst parameter H∈(0, 1), by means of its representation as a Volterra Gaussian process. This approach yields some algebraic and computational simplifications with respect to [Stochastic Process. Appl. 120 (2010) 1444–1472], where the construction of a rough path over B was first introduced.

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David Nualart. Samy Tindel. "A construction of the rough path above fractional Brownian motion using Volterra’s representation." Ann. Probab. 39 (3) 1061 - 1096, May 2011. https://doi.org/10.1214/10-AOP578

Information

Published: May 2011
First available in Project Euclid: 16 March 2011

zbMATH: 1219.60041
MathSciNet: MR2789583
Digital Object Identifier: 10.1214/10-AOP578

Subjects:
Primary: 60G15 , 60H05 , 60H07

Keywords: fractional Brownian motion , multiple stochastic integrals , Rough paths theory

Rights: Copyright © 2011 Institute of Mathematical Statistics

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Vol.39 • No. 3 • May 2011
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