Displaying similar documents to “Stochastic integration with respect to Volterra processes”

Stochastic calculus with respect to fractional Brownian motion

David Nualart (2006)

Annales de la faculté des sciences de Toulouse Mathématiques

Similarity:

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...

Ergodicity of hypoelliptic SDEs driven by fractional brownian motion

M. Hairer, N. S. Pillai (2011)

Annales de l'I.H.P. Probabilités et statistiques

Similarity:

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...

On the regularity of stochastic currents, fractional brownian motion and applications to a turbulence model

Franco Flandoli, Massimiliano Gubinelli, Francesco Russo (2009)

Annales de l'I.H.P. Probabilités et statistiques

Similarity:

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...

Probabilistic models for vortex filaments based on fractional brownian motion.

David Nualart, Carles Rovira, Samy Tindel (2001)

RACSAM

Similarity:

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.