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

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.

- 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**

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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