Fractional Ornstein-Uhlenbeck processes.
Cheridito, Patrick, Kawaguchi, Hideyuki, Maejima, Makoto (2003)
Electronic Journal of Probability [electronic only]
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Cheridito, Patrick, Kawaguchi, Hideyuki, Maejima, Makoto (2003)
Electronic Journal of Probability [electronic only]
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Aurzada, Frank, Lifshits, Mikhail (2009)
Electronic Journal of Probability [electronic only]
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Bojdecki, Tomasz, Gorostiza, Luis G., Talarczyk, Anna (2007)
Electronic Communications in Probability [electronic only]
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Michna, Zbigniew (1998)
Journal of Applied Mathematics and Stochastic Analysis
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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.
Matsui, Muneya, Shieh, Narn-Rueih (2009)
Electronic Journal of Probability [electronic only]
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Hambly, Ben M., Jones, Liza A. (2007)
Electronic Journal of Probability [electronic only]
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Yimin Xiao (2006)
Annales de la faculté des sciences de Toulouse Mathématiques
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In this survey, we first review various forms of local nondeterminism and sectorial local nondeterminism of Gaussian and stable random fields. Then we give sufficient conditions for Gaussian random fields with stationary increments to be strongly locally nondeterministic (SLND). Finally, we show some applications of SLND in studying sample path properties of -Gaussian random fields. The class of random fields to which the results are applicable includes fractional Brownian motion, the...
Boufoussi, Brahim, Dozzi, Marco E., Guerbaz, Raby (2008)
Electronic Journal of Probability [electronic only]
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Laure Coutin, Monique Pontier (2007)
ESAIM: Probability and Statistics
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A stochastic “Fubini” lemma and an approximation theorem for integrals on the plane are used to produce a simulation algorithm for an anisotropic fractional Brownian sheet. The convergence rate is given. These results are valuable for any value of the Hurst parameters Finally, the approximation process is iterative on the quarter plane A sample of such simulations can be used to test estimators of the parameters = 1,2.