Power variation of multiple fractional integrals
Constantin Tudor, Maria Tudor (2007)
Open Mathematics
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Constantin Tudor, Maria Tudor (2007)
Open Mathematics
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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, 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.
Lanjri Zadi, Noureddine, Nualart, David (2003)
Electronic Communications in Probability [electronic only]
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Dai, W., Heyde, C.C. (1996)
Journal of Applied Mathematics and Stochastic Analysis
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Istas, Jacques (2005)
Electronic Communications in Probability [electronic only]
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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.
Laure Coutin, Monique Pontier (2007)
ESAIM: Probability and Statistics
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A stochastic “Fubini” lemma and an approximation theorem for integrals on the plane are used to produce a simulation algorithm for an anisotropic fractional Brownian sheet. The convergence rate is given. These results are valuable for any value of the Hurst parameters Finally, the approximation process is iterative on the quarter plane A sample of such simulations can be used to test estimators of the parameters = 1,2.
Zili, Mounir (2006)
Journal of Applied Mathematics and Stochastic Analysis
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Cheridito, Patrick, Kawaguchi, Hideyuki, Maejima, Makoto (2003)
Electronic Journal of Probability [electronic only]
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Anh, V. V., McVinish, R. (2003)
Journal of Applied Mathematics and Stochastic Analysis
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