Fractional Ornstein-Uhlenbeck processes.
Cheridito, Patrick, Kawaguchi, Hideyuki, Maejima, Makoto (2003)
Electronic Journal of Probability [electronic only]
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Displaying similar documents to “Invariance principle, multifractional gaussian processes and long-range dependence”
Fractional Ornstein-Uhlenbeck processes.
On the small deviation problem for some iterated processes.
Aurzada, Frank, Lifshits, Mikhail (2009)
Electronic Journal of Probability [electronic only]
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Some extensions of fractional Brownian motion and sub-fractional Brownian motion related to particle systems.
Bojdecki, Tomasz, Gorostiza, Luis G., Talarczyk, Anna (2007)
Electronic Communications in Probability [electronic only]
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Self-similar processes in collective risk theory.
Michna, Zbigniew (1998)
Journal of Applied Mathematics and Stochastic Analysis
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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.
On the exponentials of fractional Ornstein-Uhlenbeck processes.
Matsui, Muneya, Shieh, Narn-Rueih (2009)
Electronic Journal of Probability [electronic only]
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Number variance from a probabilistic perspective: infinite systems of independent Brownian motions and symmetric -stable processes.
Hambly, Ben M., Jones, Liza A. (2007)
Electronic Journal of Probability [electronic only]
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Properties of local-nondeterminism of Gaussian and stable random fields and their applications
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...
Path properties of a class of locally asymptotically self similar processes.
Boufoussi, Brahim, Dozzi, Marco E., Guerbaz, Raby (2008)
Electronic Journal of Probability [electronic only]
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Approximation of the fractional Brownian sheet Ornstein-Uhlenbeck sheet
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.
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 -Statistics.