Stochastic integral of divergence type with respect to fractional brownian motion with Hurst parameter
Patrick Cheridito, David Nualart (2005)
Annales de l'I.H.P. Probabilités et statistiques
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Patrick Cheridito, David Nualart (2005)
Annales de l'I.H.P. Probabilités et statistiques
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Philippe Carmona, Laure Coutin, Gérard Montseny (2003)
Annales de l'I.H.P. Probabilités et statistiques
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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...
M. Hairer, N. S. Pillai (2011)
Annales de l'I.H.P. Probabilités et statistiques
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We demonstrate that stochastic differential equations (SDEs) driven by fractional brownian motion with Hurst parameter >½ have similar ergodic properties as SDEs driven by standard brownian motion. The focus in this article is on hypoelliptic systems satisfying Hörmander’s condition. We show that such systems enjoy a suitable version of the strong Feller property and we conclude that under a standard controllability condition they admit a unique stationary solution that is physical...
Franco Flandoli, Massimiliano Gubinelli, Francesco Russo (2009)
Annales de l'I.H.P. Probabilités et statistiques
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We study the pathwise regularity of the map ↦()= 〈( ), d 〉, where is a vector function on ℝ belonging to some Banach space , is a stochastic process and the integral is some version of a stochastic integral defined via regularization. A continuous version of this map, seen as a random element of the topological dual of will be called . We give sufficient conditions for the current to live in some Sobolev space of distributions...
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.