Stochastic processes in the spaces $D_{V,W}$
Authors:
Yu. V. Kozachenko and O. M. Moklyachuk
Translated by:
Oleg Klesov
Journal:
Theor. Probability and Math. Statist. 82 (2011), 43-56
MSC (2010):
Primary 60G07
DOI:
https://doi.org/10.1090/S0094-9000-2011-00826-5
Published electronically:
August 2, 2011
MathSciNet review:
2790483
Full-text PDF Free Access
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Abstract: We introduce the spaces of random variables $D_{V,W}$. We study the conditions for the convergence of series and the distribution of the supremum of stochastic processes in these spaces.
References
- 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
- Yu. V. Kozachenko, On the distribution of the supremum of random processes in quasi-Banach $K_\sigma $-spaces, Ukraïn. Mat. Zh. 51 (1999), no. 7, 918–930 (Ukrainian, with English and Ukrainian summaries); English transl., Ukrainian Math. J. 51 (1999), no. 7, 1029–1043 (2000). MR 1727696, DOI https://doi.org/10.1007/BF02592039
- 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 and E. I. Ostrovskiĭ, Banach spaces of random variables of sub-Gaussian type, Teor. Veroyatnost. i Mat. Statist. 32 (1985), 42–53, 134 (Russian). MR 882158
- 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
- V. V. Buldygin and Yu. V. Kozachenko, Metric Characterization of Random Variables and Random Processes, TViMS, Kiev, 1998; English transl., American Mathematical Society, Providence, RI, 2000. MR 1743716 (2001g:60089)
- Yu. V. Kozachenko, Distribution of the supremum of random processes from quasi-Banach $K_\sigma$-spaces, Ukrain. Mat. Zh. 51 (1999), no. 7, 918–930; English transl. in Ukrainian Math. J. 51 (1999), 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)
- 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; English transl. in Ukrainian Math. J. 37 (1985), no. 3, 209–213. MR 795565 (87m:60095)
- 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, Institute of Mathematics, Academy of Sciences of Ukrain. SSR, Kiev, 1986, pp. 4–11. (Russian) MR 895373 (88g:60101)
- Yu. V. Kozachenko and E. I. Ostrovskiĭ, Banach spaces of sub-Gaussian random variables, Teor. Veroyatnost. i Mat. Statist. 32 (1985), 42–53; English transl. in Theory Probab. Math. Statist. 32 (1986), 45–56. MR 882158 (88e:60009)
- 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)
- Yu. V. Kozachenko, Random processes in Orlicz spaces. II, Teor. Veroyatnost. i Mat. Statist. 31 (1984), 44–50; English transl. in Theory Probab. Math. Statist. 31 (1985), 51–58. MR 816125 (87b:60063)
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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,
prenorm,
quasinorm,
pre-Banach space,
quasi-Banach space,
the convergence of series
Received by editor(s):
January 21, 2010
Published electronically:
August 2, 2011
Additional Notes:
The first author is grateful to the Department of Mathematics and Statistics of the University “La Trobe”, Melbourne, for support in the framework of the research grant “Stochastic Approximation in Finance and Signal Processing”
Article copyright:
© Copyright 2011
American Mathematical Society
