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
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
Full-text PDF Free Access
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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
- 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.
- Yu. V. Kozachenko and O. A. Pashko, Models of Stochastic Processes, Kyiv University, Kyiv, 1999. (Ukrainian)
- Yuri Kozachenko and Iryna Rozora, Simulation of Gaussian stochastic processes, Random Oper. Stochastic Equations 11 (2003), no. 3, 275โ296. MR 2009187, DOI https://doi.org/10.1163/156939703771378626
- V. V. Buldygin and Yu. V. Kozachenko, Metric characterization of random variables and random processes, Translations of Mathematical Monographs, vol. 188, American Mathematical Society, Providence, RI, 2000. Translated from the 1998 Russian original by V. Zaiats. MR 1743716
- Yurii V. Kozachenko and Oksana I. Vasilik, On the distribution of suprema of ${\rm Sub}_\phi (\Omega )$ random processes, Proceedings of the Donetsk Colloquium on Probability Theory and Mathematical Statistics (1998), 1998, pp. 147โ160. MR 2026624
References
- 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.
- Yu. V. Kozachenko and O. A. Pashko, Models of Stochastic Processes, Kyiv University, Kyiv, 1999. (Ukrainian)
- Yu. Kozachenko and I. Rozora, Simulation of stochastic Gaussian processes, Random Operators Stoch. Equations 11 (2003), no. 3, 275โ296. MR 2009187 (2004i:60050)
- 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)
- 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. 1โ2, 147โ160. 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:
yvk\@univ.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
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
