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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

 

Lipschitz conditions for $ \operatorname{Sub}_\varphi(\Omega)$-processes and applications to weakly self-similar processes with stationary increments


Authors: Yuriĭ Kozachenko, Tommi Sottinen and Ol’ga Vasylyk
Translated by: the authors
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 82 (2010).
Journal: Theor. Probability and Math. Statist. 82 (2011), 57-73
MSC (2010): Primary 60G17, 60G18
Published electronically: August 2, 2011
MathSciNet review: 2790484
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Abstract | References | Similar Articles | Additional Information

Abstract: We study the Lipschitz continuity of generalized sub-Gaussian processes and provide estimates for the distribution of the norms of such processes. The results are applied to the case of weakly self-similar generalized sub-Gaussian processes with stationary increments (the fractional Brownian motion is a particular case of these processes).


References [Enhancements On Off] (What's this?)

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Additional Information

Yuriĭ Kozachenko
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 2, Kiev 03127, Ukraine
Email: yvk@univ.kiev.ua

Tommi Sottinen
Affiliation: University of Vaasa, Faculty of Technology, Department of Mathematics and Statistics, P.O. Box 700, FIN-65101 Vaasa, Finland
Email: tommi.sottinen@uwasa.fi

Ol’ga Vasylyk
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 2, Kiev 03127, Ukraine
Email: ovasylyk@univ.kiev.ua

DOI: http://dx.doi.org/10.1090/S0094-9000-2011-00827-7
PII: S 0094-9000(2011)00827-7
Keywords: Self-similarity, fractional Brownian motion, generalized sub-Gaussian processes, Lipschitz continuity
Received by editor(s): December 16, 2009
Published electronically: August 2, 2011
Additional Notes: The first author is indebted to the Department of Mathematics and Statistics of the University “La Trobe”, Melbourne, for the support in the framework of the research grant “Stochastic approximation in finance and signal-processing”.
Article copyright: © Copyright 2011 American Mathematical Society