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

Published electronically:
February 2, 2012

MathSciNet review:
2768851

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

**1.**Yu. V. Kozachenko and O. M. Moklyachuk,*Random processes in the spaces 𝐷_{𝑉,𝑊}*, Teor. Ĭmovīr. Mat. Stat.**82**(2010), 56–66 (Ukrainian, with English, Russian and Ukrainian summaries); English transl., Theory Probab. Math. Statist.**82**(2011), 43–56. MR**2790483**, 10.1090/S0094-9000-2011-00826-5**2.**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****3.**Yu. V. Kozachenko,*On the distribution of the supremum of random processes in quasi-Banach 𝐾_{𝜎}-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**, 10.1007/BF02592039**4.**V. V. Buldygin,*Skhodimost sluchainykh elementov v topologicheskikh prostranstvakh*, “Naukova Dumka”, Kiev, 1980 (Russian). MR**734899****5.**E. A. Abzhanov and Yu. V. Kozachenko,*Some properties of random processes in Banach 𝐾_{𝜎}-spaces*, Ukrain. Mat. Zh.**37**(1985), no. 3, 275–280, 403 (Russian). MR**795565****6.**E. A. Abzhanov and Yu. V. Kozachenko,*Random processes in quasi-Banach 𝐾_{𝜎}-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****7.**Yu. V. Kozachenko,*Random processes in Orlicz spaces. I*, Teor. Veroyatnost. i Mat. Statist.**30**(1984), 92–107, 152 (Russian). MR**800835****8.**Yu. V. Kozachenko,*Random processes in Orlicz spaces. II*, Teor. Veroyatnost. i Mat. Statist.**31**(1984), 44–50, 143 (Russian). MR**816125**

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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/S0094-9000-2012-00844-2

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):
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