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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Displaying similar documents to “On the exponentials of fractional Ornstein-Uhlenbeck processes.”
Number variance from a probabilistic perspective: infinite systems of independent Brownian motions and symmetric -stable processes.
Fractional Ornstein-Uhlenbeck processes.
Cheridito, Patrick, Kawaguchi, Hideyuki, Maejima, Makoto (2003)
Electronic Journal of Probability [electronic only]
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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.
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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Self-similar processes in collective risk theory.
Michna, Zbigniew (1998)
Journal of Applied Mathematics and Stochastic Analysis
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On the small deviation problem for some iterated processes.
Aurzada, Frank, Lifshits, Mikhail (2009)
Electronic Journal of Probability [electronic only]
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Long memory and self-similar processes
Gennady Samorodnitsky (2006)
Annales de la faculté des sciences de Toulouse Mathématiques
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This paper is a survey of both classical and new results and ideas on long memory, scaling and self-similarity, both in the light-tailed and heavy-tailed cases.