Stochastic processes in the spaces 
Authors:
Yu. V. Kozachenko and O. M. Moklyachuk
Translated by:
Oleg Klesov
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom 82 (2010).
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
Abstract | References | Similar Articles | Additional Information
Abstract: We introduce the spaces of random variables 
. We study the conditions for the convergence of series and the distribution of the supremum of stochastic processes in these spaces.
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-spaces, Ukrain. Mat. Zh. 51 (1999), no. 7, 918-930; English transl. in Ukrainian Math. J. 51 (1999), no. 7, 1029-1043. 
-spaces, Ukrain. Mat. Zh. 37 (1985), no. 3, 275-280; English transl. in Ukrainian Math. J. 37 (1985), no. 3, 209-213. 
-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) Retrieve articles in Theory of Probability and Mathematical Statistics with MSC (2010): 60G07
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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
DOI:
https://doi.org/10.1090/S0094-9000-2011-00826-5
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
