Singularity functions for fractional processes : application to the fractional brownian sheet
Serge Cohen, Xavier Guyon, Olivier Perrin, Monique Pontier (2006)
Annales de l'I.H.P. Probabilités et statistiques
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Serge Cohen, Xavier Guyon, Olivier Perrin, Monique Pontier (2006)
Annales de l'I.H.P. Probabilités et statistiques
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Antoine Ayache, Narn-Rueih Shieh, Yimin Xiao (2011)
Annales de l'I.H.P. Probabilités et statistiques
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By using a wavelet method we prove that the harmonisable-type -parameter multifractional brownian motion (mfBm) is a locally nondeterministic gaussian random field. This nice property then allows us to establish joint continuity of the local times of an (, )-mfBm and to obtain some new results concerning its sample path behavior.
Mihai Gradinaru, Ivan Nourdin, Francesco Russo, Pierre Vallois (2005)
Annales de l'I.H.P. Probabilités et statistiques
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Mihai Gradinaru, Ivan Nourdin (2009)
Annales de l'I.H.P. Probabilités et statistiques
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Weighted power variations of fractional brownian motion are used to compute the exact rate of convergence of some approximating schemes associated to one-dimensional stochastic differential equations (SDEs) driven by . The limit of the error between the exact solution and the considered scheme is computed explicitly.
P. Friz, T. Lyons, D. Stroock (2006)
Annales de l'I.H.P. Probabilités et statistiques
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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.