Sample continuity and modeling of stochastic processes from the spaces $D_{V,W}$
Authors:
Yu. V. Kozachenko and O. M. Moklyachuk
Translated by:
O. Klesov
Journal:
Theor. Probability and Math. Statist. 83 (2011), 95-110
MSC (2010):
Primary 60G07
DOI:
https://doi.org/10.1090/S0094-9000-2012-00844-2
Published electronically:
February 2, 2012
MathSciNet review:
2768851
Full-text PDF Free Access
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Abstract: Random sequences and stochastic processes belonging to the spaces $D_{V,W}$ are studied in the paper. Conditions for the sample continuity of such processes are found. The convergence of series of random variables belonging to the spaces $D_{V,W}$ are considered. Models of stochastic processes belonging to the spaces $D_{V,W}$ are studied. Several examples of models are given.
References
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- 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
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- V. V. Buldygin, Skhodimost′sluchaĭ nykh èlementov v topologicheskikh prostranstvakh, “Naukova Dumka”, Kiev, 1980 (Russian). MR 734899
- E. A. Abzhanov and Yu. V. Kozachenko, Some properties of random processes in Banach $K_\sigma $-spaces, Ukrain. Mat. Zh. 37 (1985), no. 3, 275–280, 403 (Russian). MR 795565
- E. A. Abzhanov and Yu. V. Kozachenko, Random processes in quasi-Banach $K_\sigma $-spaces of random variables, Probabilistic methods for the investigation of systems with an infinite number of degrees of freedom (Russian), Akad. Nauk Ukrain. SSR, Inst. Mat., Kiev, 1986, pp. 4–11, i (Russian). MR 895373
- Yu. V. Kozachenko, Random processes in Orlicz spaces. I, Teor. Veroyatnost. i Mat. Statist. 30 (1984), 92–107, 152 (Russian). MR 800835
- Yu. V. Kozachenko, Random processes in Orlicz spaces. II, Teor. Veroyatnost. i Mat. Statist. 31 (1984), 44–50, 143 (Russian). MR 816125
References
- Yu. V. Kozachenko and O. M. Moklyachuk, Stochastic processes in the spaces $D_{V,W}$, Teor. Imovir. Mat. Stat. 82 (2010), 56–66; English transl. in Theor. Probability and Math. Statist. 82 (2011), 43–56. MR 2790483 (2011m:60101)
- V. V. Buldygin and Yu. V. Kozachenko, Metric Characterization of Random Variables and Random Processes, TViMS, Kiev, 1998; English transl., American Mathematical Society, Providence, Rhode Island, 2000. MR 1743716 (2001g:60089)
- Yu. V. Kozachenko, On the distribution of the supremum of random processes in quasi-Banach $K_\sigma$-spaces, Ukrain. Mat. Zh. 51 (1999), no. 7, 918–930; English transl. in Ukrainian Math. J. 51 (2000), no. 7, 1029–1043. MR 1727696 (2000k:60066)
- V. V. Buldygin, Convergence of Random Elements in Topological Spaces, Naukova Dumka, Kiev, 1980. (Russian) MR 734899 (84m:60011)
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- E. A. Abzhanov and Yu. V. Kozachenko, Random processes in $K_\sigma$-spaces of random variables, Probabilistic Methods for the Investigation of Systems with an Infinite Number of Degrees of Freedom (A. V. Skorokhod, ed.), Institute of Mathematics, Academy of Science of Ukrain. SSR, Kiev, 1986, pp. 4–11, Russian. MR 895373 (88g:60101)
- Yu. V. Kozachenko, Random processes in Orlicz spaces. I, Teor. Veroyatnost. i Mat. Statist. 30 (1984), 92–107; English transl. in Theory Probab. Math. Statist. 30 (1985), 103–117. MR 800835 (86m:60111)
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Additional Information
Yu. V. Kozachenko
Affiliation:
Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 2, Kiev 03127, Ukraine
Email:
yvk@univ.kiev.ua
O. M. Moklyachuk
Affiliation:
Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 2, Kiev 03127, Ukraine
Email:
omoklyachuk@ukr.net
Keywords:
Stochastic processes,
modeling of stochastic processes,
pre-norm,
quasi-norm,
pre-Banach spaces,
quasi-Banach spaces,
spaces $D_{V,W}$
Received by editor(s):
July 19, 2010
Published electronically:
February 2, 2012
Additional Notes:
The first author is grateful to the Department of Mathematics and Statistics, La Trobe University, Melbourne, for support in the framework of a research grant “Stochastic Approximation in Finance and Signal Processing”
Article copyright:
© Copyright 2012
American Mathematical Society
