Abstract
We have proved recently that fractional Brownian motions with Hurst parameter H in (0, 1/2) satisfy a remarkable property: their squares are infinitely divisible. In the Brownian motion case (the case H = 1/2), this property is completely understood thanks to stochastic calculus arguments. We try here to take advantage of the stochastic calculus recently developed with respect to fractional Brownian motion, to construct analogous explanations of this property in the case \(H \not = 1/2\).
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© 2005 Springer-Verlag Berlin/Heidelberg
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Eisenbaum, N., Tudor, C.A. (2005). On Squared Fractional Brownian Motions. In: Émery, M., Ledoux, M., Yor, M. (eds) Séminaire de Probabilités XXXVIII. Lecture Notes in Mathematics, vol 1857. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31449-3_19
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DOI: https://doi.org/10.1007/978-3-540-31449-3_19
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23973-4
Online ISBN: 978-3-540-31449-3
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