Some extensions of fractional Brownian motion and sub-fractional Brownian motion related to particle systems.
Bojdecki, Tomasz, Gorostiza, Luis G., Talarczyk, Anna (2007)
Electronic Communications in Probability [electronic only]
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Bojdecki, Tomasz, Gorostiza, Luis G., Talarczyk, Anna (2007)
Electronic Communications in Probability [electronic only]
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David Nualart, Aurel Rascanu (2002)
Collectanea Mathematica
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A global existence and uniqueness result of the solution for multidimensional, time dependent, stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H > 1/2 is proved. It is shown, also, that the solution has finite moments. The result is based on a deterministic existence and uniqueness theorem whose proof uses a contraction principle and a priori estimates.
Istas, Jacques (2005)
Electronic Communications in Probability [electronic only]
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Aurzada, Frank, Lifshits, Mikhail (2009)
Electronic Journal of Probability [electronic only]
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Baudoin, Fabrice, Coutin, Laure (2008)
Electronic Journal of Probability [electronic only]
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David Nualart (2006)
Annales de la faculté des sciences de Toulouse Mathématiques
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Fractional Brownian motion (fBm) is a centered self-similar Gaussian process with stationary increments, which depends on a parameter called the Hurst index. In this conference we will survey some recent advances in the stochastic calculus with respect to fBm. In the particular case , the process is an ordinary Brownian motion, but otherwise it is not a semimartingale and Itô calculus cannot be used. Different approaches have been introduced to construct stochastic integrals with...
David Nualart, Carles Rovira, Samy Tindel (2001)
RACSAM
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Se introduce una estructura de vorticidad basada en el movimiento browniano fraccionario con parámetro de Hurst H > 1/2 . El objeto de esta nota es presentar el siguiente resultado: Bajo una condición de integrabilidad adecuada sobre la medida ρ que controla la concentración de la vorticidad a lo largo de los filamentos, la energía cinética de la configuración está bien definida y tiene momentos de todos los órdenes.
A. Deya, A. Neuenkirch, S. Tindel (2012)
Annales de l'I.H.P. Probabilités et statistiques
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In this article, we study the numerical approximation of stochastic differential equations driven by a multidimensional fractional Brownian motion (fBm) with Hurst parameter greater than 1/3. We introduce an implementable scheme for these equations, which is based on a second-order Taylor expansion, where the usual Lévy area terms are replaced by products of increments of the driving fBm. The convergence of our scheme is shown by means of a combination of rough paths techniques and error...
Cheridito, Patrick, Kawaguchi, Hideyuki, Maejima, Makoto (2003)
Electronic Journal of Probability [electronic only]
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Constantin Tudor, Maria Tudor (2007)
Open Mathematics
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