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Sample continuity and modeling of stochastic processes from the spaces 
Authors:
Yu. V. Kozachenko and O. M. Moklyachuk
Translated by:
O. Klesov
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom 83 (2010).
Journal:
Theor. Probability and Math. Statist. 83 (2011), 95-110
MSC (2010):
Primary 60G07
Posted:
February 2, 2012
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Abstract: Random sequences and stochastic processes belonging to the spaces  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  are considered. Models of stochastic processes belonging to the spaces  are studied. Several examples of models are given.
References
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- 2.
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)
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Mat. Zh. 51 (1999), no. 7, 918–930 (Ukrainian,
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51 (1999), no. 7, 1029–1043 (2000). MR 1727696
(2000k:60066), http://dx.doi.org/10.1007/BF02592039
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V. V. Buldygin, Convergence of Random Elements in Topological Spaces, Naukova Dumka, Kiev, 1980. (Russian) MR 734899 (84m:60011)
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- 8.
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
DOI:
http://dx.doi.org/10.1090/S0094-9000-2012-00844-2
PII:
S 0094-9000(2012)00844-2
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):
19/JUL/2010
Posted:
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
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