Displaying similar documents to “m-order integrals and generalized Itô's formula ; the case of a fractional brownian motion with any Hurst index”

Stochastic calculus with respect to fractional Brownian motion

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 H ∈ ( 0 , 1 ) 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 H = 1 / 2 , 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...

Differential equations driven by fractional Brownian motion.

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.

Probabilistic models for vortex filaments based on fractional brownian motion.

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.