Theory of Probability and Mathematical Statistics

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ISSN 1547-7363(e) ISSN 0094-9000(p)

Accuracy and reliability of models of stochastic processes of the space $\mathrm{Sub}_\varphi(\Omega)$

Author(s): Yu. V. Kozachenko; I. V. Rozora
Translated by: Oleg Klesov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, vipusk 71 (2004).
Journal: Theor. Probability and Math. Statist. No. 71 (2005), 105-117.
MSC (2000): Primary 68U20; Secondary 60G10
Posted: December 28, 2005
MathSciNet review: 2144324
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Abstract | References | Similar articles | Additional information

Abstract: Stochastic processes of the space $\mathrm{Sub}_\varphi(\Omega)$ are considered in the paper. We prove upper bounds for large deviation probabilities and construct models of stochastic processes in the space with a given accuracy and reliability. Strongly sub-Gaussian processes are also considered as a particular case.

References:

1.: Yu. Kozachenko, T. Sottinen, and O. Vasylyk, Simulation of Weakly Self-Similar Stationary Increment $\mathrm{Sub}_{\varphi}(\Omega)$ -Processes: a Series Expansion Approach, Reports of the Department of Mathematics, Preprint 398, University of Helsinki, October 2004.
2.: Yu. V. Kozachenko and O. A. Pashko, Models of Stochastic Processes, Kyiv University, Kyiv, 1999. (Ukrainian)
3.: Yu. Kozachenko and I. Rozora, Simulation of stochastic Gaussian processes, Random Operators Stoch. Equations 11 (2003), no. 3, 275-296. MR 2009187 (2004i:60050)
4.: V. V. Buldygin and Yu. V. Kozachenko, Metric Characterization of Random Variables and Random Processes, TViMS, Kiev, 1998; English transl. AMS, Providence, 2000.MR 1743716 (2001g:60089)
5.: Yu. V. Kozachenko and O. I. Vasylyk, On the distribution of suprema of $\mathrm{Sub}_\varphi(\Omega)$ random processes, Theory Stoch. Processes 4(20) (1998), no. 1-2, 147-160.MR 2026624 (2004k:60094)

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Additional Information:

Yu. V. Kozachenko
Affiliation: Department of Probability Theory and Mathematical Statistics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine
Email: yvkuniv.kiev.ua

I. V. Rozora
Affiliation: Department of Probability Theory and Mathematical Statistics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine
Email: irozora@bigmir.net

DOI: 10.1090/S0094-9000-05-00651-4
PII: S 0094-9000(05)00651-4
Received by editor(s): 27/FEB/2004
Posted: December 28, 2005
Additional Notes: Supported in part by NATO grant PST.CLG.980408.
Copyright of article: Copyright 2005, American Mathematical Society

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