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Displaying similar documents to “Enhanced Gaussian processes and applications”

Differential equations driven by gaussian signals

Peter Friz, Nicolas Victoir (2010)

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

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We consider multi-dimensional gaussian processes and give a new condition on the covariance, simple and sharp, for the existence of Lévy area(s). gaussian rough paths are constructed with a variety of weak and strong approximation results. Together with a new RKHS embedding, we obtain a powerful – yet conceptually simple – framework in which to analyze differential equations driven by gaussian signals in the rough paths sense.

Invariance principle, multifractional gaussian processes and long-range dependence

Serge Cohen, Renaud Marty (2008)

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

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This paper is devoted to establish an invariance principle where the limit process is a multifractional gaussian process with a multifractional function which takes its values in (1/2, 1). Some properties, such as regularity and local self-similarity of this process are studied. Moreover the limit process is compared to the multifractional brownian motion.