On the small deviation problem for some iterated processes.
Aurzada, Frank, Lifshits, Mikhail (2009)
Electronic Journal of Probability [electronic only]
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Displaying similar documents to “Self-similar processes in collective risk theory.”
On the small deviation problem for some iterated processes.
Fractional Ornstein-Uhlenbeck processes.
Cheridito, Patrick, Kawaguchi, Hideyuki, Maejima, Makoto (2003)
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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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.
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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A solution of an equation for indexed functions
Petr Lachout (2004)
Acta Universitatis Carolinae. Mathematica et Physica
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Long-range dependence through gamma-mixed Ornstein-Uhlenbeck process.
Iglói, E., Terdik, G. (1999)
Electronic Journal of Probability [electronic only]
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On the exponentials of fractional Ornstein-Uhlenbeck processes.
Matsui, Muneya, Shieh, Narn-Rueih (2009)
Electronic Journal of Probability [electronic only]
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Small deviations of iterated processes in the space of trajectories
Andrei Frolov (2013)
Open Mathematics
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We derive logarithmic asymptotics of probabilities of small deviations for iterated processes in the space of trajectories. We find conditions under which these asymptotics coincide with those of processes generating iterated processes. When these conditions fail the asymptotics are quite different.
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.