Stochastic integration with respect to Volterra processes
L. Decreusefond (2005)
Annales de l'I.H.P. Probabilités et statistiques
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L. Decreusefond (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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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...
Yaozhong Hu (2002)
Annales de l'I.H.P. Probabilités et statistiques
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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...