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Theory of Probability and Mathematical Statistics

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


Authors: Yu. V. Kozachenko and I. V. Rozora
Translated by: Oleg Klesov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 71 (2004).
Journal: Theor. Probability and Math. Statist. 71 (2005), 105-117
MSC (2000): Primary 68U20; Secondary 60G10
DOI: https://doi.org/10.1090/S0094-9000-05-00651-4
Published electronically: 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 $ C[0,1]$ with a given accuracy and reliability. Strongly sub-Gaussian processes are also considered as a particular case.


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

  • 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: https://doi.org/10.1090/S0094-9000-05-00651-4
Received by editor(s): February 27, 2004
Published electronically: December 28, 2005
Additional Notes: Supported in part by NATO grant PST.CLG.980408.
Article copyright: © Copyright 2005 American Mathematical Society