Displaying similar documents to “Differential equations driven by gaussian signals”

Enhanced Gaussian processes and applications

Laure Coutin, Nicolas Victoir (2009)

ESAIM: Probability and Statistics

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We propose some construction of enhanced Gaussian processes using Karhunen-Loeve expansion. We obtain a characterization and some criterion of existence and uniqueness. Using rough-path theory, we derive some Wong-Zakai Theorem.

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.

Asymptotic behavior of the empirical process for gaussian data presenting seasonal long-memory

Mohamedou Ould Haye (2002)

ESAIM: Probability and Statistics

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We study the asymptotic behavior of the empirical process when the underlying data are gaussian and exhibit seasonal long-memory. We prove that the limiting process can be quite different from the limit obtained in the case of regular long-memory. However, in both cases, the limiting process is degenerated. We apply our results to von–Mises functionals and U -Statistics.

Stochastic differential equations driven by processes generated by divergence form operators I: a Wong-Zakai theorem

Antoine Lejay (2006)

ESAIM: Probability and Statistics

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We show in this article how the theory of “rough paths” allows us to construct solutions of differential equations (SDEs) driven by processes generated by divergence-form operators. For that, we use approximations of the trajectories of the stochastic process by piecewise smooth paths. A result of type Wong-Zakai follows immediately.