Small deviations for fractional stable processes
Mikhail Lifshits, Thomas Simon (2005)
Annales de l'I.H.P. Probabilités et statistiques
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Mikhail Lifshits, Thomas Simon (2005)
Annales de l'I.H.P. Probabilités et statistiques
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Maejima, Makoto, Yamamoto, Kenji (2003)
Electronic Journal of Probability [electronic only]
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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.
Li, Wenbo V. (1999)
Electronic Communications in Probability [electronic only]
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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.
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.
Cheridito, Patrick, Kawaguchi, Hideyuki, Maejima, Makoto (2003)
Electronic Journal of Probability [electronic only]
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Darses, Sebastien, Saussereau, Bruno (2007)
Electronic Journal of Probability [electronic only]
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