Conditions for the sample continuity with probability one for square-Gaussian stochastic processes
Authors:
Yu. V. Kozachenko and I. V. Rozora
Translated by:
S. V. Kvasko
Journal:
Theor. Probability and Math. Statist. 101 (2020), 153-166
MSC (2020):
Primary 60G17; Secondary 60E05
DOI:
https://doi.org/10.1090/tpms/1118
Published electronically:
January 5, 2021
Full-text PDF
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Additional Information
Abstract: Square-Gaussian stochastic processes are considered. Sufficient conditions for the sample uniform continuity with probability one on a compact set are found for square-Gaussian processes. An estimate for the modulus of continuity of a square-Gaussian stochastic process is obtained.
References
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- Yu. V. Kozachenko and I. V. Rozora, A criterion for testing hypothesis about impulse response function, Stat. Optim. Inf. Comput. 4 (2016), no. 3, 214–232. MR 3556027, DOI https://doi.org/10.19139/soic.v4i3.222
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- Yuriy Kozachenko, Anatolii Pashko, and Olga Vasylyk, Simulation of generalized fractional Brownian motion in $C([0,T])$, Monte Carlo Methods Appl. 24 (2018), no. 3, 179–192. MR 3849695, DOI https://doi.org/10.1515/mcma-2018-0016
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- Iryna Rozora and Mariia Lyzhechko, On the modeling of linear system input stochastic processes with given accuracy and reliability, Monte Carlo Methods Appl. 24 (2018), no. 2, 129–137. MR 3808323, DOI https://doi.org/10.1515/mcma-2018-0011
References
- V. V. Buldygin and Yu. V. Kozachenko, Metric characterization of random variables and random processes, TBiMC, Kiev, 1998; English transl. American Mathematical Society, Providence, RI, 2000. MR 1743716
- R. M. Dudley, The sizes of compact subsets of Hilbert space and continuity of Gaussian processes, J. Funct. Anal. 1 (1967), 290–330. MR 0220340
- I. I. Gikhman and A. V. Skorokhod, Introduction to the Theory of Random Processes, vol. 1, “Naukà”, Moscow, 1977. (In Russian) MR 0651014
- Yu. V. Kozachenko and O. M. Moklyachuk, Large deviation probabilities for square-Gaussian stochastic processes, Extremes 2 (1999), no. 3, 269–293. MR 1781940
- Yu. V. Kozachenko, O. O. Pogorilyak, I. V. Rozora, and A. M. Tegza, Simulation of Stochastic Processes with Given Accuracy and Reliability, ISTE Press/Elsevier, 2016. MR 3644192
- Yu. V. Kozachenko and I. V. Rozora, A criterion for testing hypothesis about impulse response function, Stat. Optim. Inf. Comput. 4 (2016), no. 3, 214–232. MR 3556027
- Yu. V. Kozachenko and O. V. Stus, Square-Gaussian random processes and estimators of covariance functions, Math. Comm. 3 (1998), no. 1, 83–94. MR 1648867
- A. O. Pashko and I. V. Rozora, Accuracy of simulation for the network traffic in the form of fractional Brownian motion, 14th International Conference on Advanced Trends in Radioelectronics, Telecommunications and Computer Engineering, TCSET, Proceedings, 2018, pp. 840–845. MR 3849695
- I. V. Rozora, Statistical hypothesis testing for the shape of impulse response function, Comm. Stat. Theory and Methods 47 (2018), no. 6, 1459–1474. MR 3756253
- I. V. Rozora and M. V. Lyzhechko, On the modeling of linear system input stochastic processes with given accuracy and reliability, Monte Carlo Methods Appl. 24 (2018), no. 2, 129–137. MR 3808323
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Additional Information
Yu. V. Kozachenko
Affiliation:
Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, Kyiv Taras Shevchenko National University, Volodymyrs’ka Street, 64/13, Kyiv 01601, Ukraine
Email:
yvk@univ.kiev.ua
I. V. Rozora
Affiliation:
Department of Applied Statistics, Faculty for Computer Science and Cybernetics, Kyiv Taras Shevchenko National University, Volodymyrs’ka Street, 64/13, Kyiv 01601, Ukraine
Email:
irozora@bigmir.net
Keywords:
Sample continuity,
modulus of continuity,
square-Gaussian stochastic processes
Received by editor(s):
August 29, 2019
Published electronically:
January 5, 2021
Article copyright:
© Copyright 2020
American Mathematical Society
