Self-similar and Markov composition structures.
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Gnedin, A., Pitman, Jim (2005)
Zapiski Nauchnykh Seminarov POMI
Baudoin, Fabrice, Coutin, Laure (2008)
Electronic Journal of Probability [electronic only]
Vladas Pipiras, Murad S. Taqqu (2010)
Discussiones Mathematicae Probability and Statistics
Kernel functions of stable, self-similar mixed moving averages are known to be related to nonsingular flows. We identify and examine here a new functional occuring in this relation and study its properties. To prove its existence, we develop a general result about semi-additive functionals related to cocycles. The functional we identify, is helpful when solving for the kernel function generated by a flow. Its presence also sheds light on the previous results on the subject.
Guangjun Shen, Litan Yan, Chao Chen (2012)
Czechoslovak Mathematical Journal
Let , be two independent, -dimensional bifractional Brownian motions with respective indices and . Assume . One of the main motivations of this paper is to investigate smoothness of the collision local time where denotes the Dirac delta function. By an elementary method we show that is smooth in the sense of Meyer-Watanabe if and only if .
Bojdecki, Tomasz, Gorostiza, Luis G., Talarczyk, Anna (2007)
Electronic Communications in Probability [electronic only]
David Nualart (2006)
Annales de la faculté des sciences de Toulouse Mathématiques
Fractional Brownian motion (fBm) is a centered self-similar Gaussian process with stationary increments, which depends on a parameter called the Hurst index. In this conference we will survey some recent advances in the stochastic calculus with respect to fBm. In the particular case , the process is an ordinary Brownian motion, but otherwise it is not a semimartingale and Itô calculus cannot be used. Different approaches have been introduced to construct stochastic integrals with respect to fBm:...
Zdzisław Brzeźniak, Jan van Neerven, Donna Salopek (2012)
Czechoslovak Mathematical Journal
Let be a Hilbert space and a Banach space. We set up a theory of stochastic integration of -valued functions with respect to -cylindrical Liouville fractional Brownian motion with arbitrary Hurst parameter . For we show that a function is stochastically integrable with respect to an -cylindrical Liouville fractional Brownian motion if and only if it is stochastically integrable with respect to an -cylindrical fractional Brownian motion. We apply our results to stochastic evolution equations...
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