Abstract
We consider a geometric rough path associated with a fractional Brownian motion with Hurst parameter H ∈] 1/4, 1/2 [. We give an approximation result in a modulus type distance, up to the second order, by means of a sequence of rough paths lying above elements of the reproducing kernel Hilbert space.
First author was supported by the grants BFM 2003-01345, HF 2003-006, Dirección General de Investigación, Ministerio de Educación y Ciencia, Spain and partially supported by the program SAB 2003-0082, Dirección General de Universidades, Ministerio de Educación y Ciencia, Spain. Second author was supported by the grants BFM 2003-01345, HF 2003-006, Dirección General de Investigación, Ministerio de Educación y Ciencia, Spain.
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© 2007 Birkhäuser Verlag Basel/Switzerland
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Millet, A., Sanz-Solé, M. (2007). Approximation of Rough Paths of Fractional Brownian Motion. In: Dalang, R.C., Russo, F., Dozzi, M. (eds) Seminar on Stochastic Analysis, Random Fields and Applications V. Progress in Probability, vol 59. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8458-6_16
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DOI: https://doi.org/10.1007/978-3-7643-8458-6_16
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-8457-9
Online ISBN: 978-3-7643-8458-6
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