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A construction of the rough path above fractional Brownian motion using Volterra’s representation
Nualart, David Tindel, Samy
Nualart, David
Tindel, Samy
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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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This is the published version, also available here: http://dx.doi.org/10.1214/10-AOP578.
Date
2011-09-01
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Institute of Mathematical Statistics
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Keywords
Rough paths theory, fractional Brownian motion, multiple stochastic integrals
Citation
Nualart, David & Tindel, Samy. "A construction of the rough path above fractional Brownian motion using Volterra’s representation." Ann. Probab. Volume 39, Number 3 (2011), 1061-1096. http://dx.doi.org/10.1214/10-AOP578.