An approximation of stochastic processes belonging to the Orlicz space in the norm of the space $C[0,\infty )$
Authors:
Yu. V. Kozachenko and O. E. Kamenshchikova
Translated by:
S. Kvasko
Journal:
Theor. Probability and Math. Statist. 88 (2014), 123-138
MSC (2010):
Primary 60G17; Secondary 60G07
DOI:
https://doi.org/10.1090/S0094-9000-2014-00923-0
Published electronically:
July 24, 2014
MathSciNet review:
3112639
Full-text PDF Free Access
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Abstract: Some bounds for the distributions of increments of Orlicz stochastic processes defined in the semiaxis $[0,\infty )$ are obtained. An approximation of such processes by integer functions of exponential type that does not exceed a number $\gamma$ is studied in the $C[0,\infty )$ metric with a given accuracy and reliability.
References
- O. Ē. Kamenshchikova and T. O. Yanevich, Approximation of $L_p(\Omega )$-processes, Teor. Ĭmovīr. Mat. Stat. 83 (2010), 59–68 (Ukrainian, with English and Ukrainian summaries); English transl., Theory Probab. Math. Statist. 83 (2011), 71–82. MR 2768849, DOI https://doi.org/10.1090/S0094-9000-2012-00842-9
- 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
- N. I. Achieser, Theory of approximation, Frederick Ungar Publishing Co., New York, 1956. Translated by Charles J. Hyman. MR 0095369
References
- O. E. Kamenshchikova and T. O. Yanevich, An approximation of $L_p(\Omega )$ processes, Teor. Imovir. Mat. Stat. 83 (2010), 59–68; English transl. in Theory Probab. Math. Statist. 83 (2011), 71–82. MR 2768849 (2011k:60114)
- V. V. Buldygin and Yu. V. Kozachenko, Metric Characterization of Random Variables and Random Processes, TViMS, Kyiv, 1998; American Mathematical Society, Providence, RI, 2000. MR 1743716 (2001g:60089)
- N. I. Achieser, Theory of approximation, “Nauka”, Moscow, 1965; English transl. of the first edition by Frederick Ungar Publishing Co., New York, 1956. MR 0095369 (20:1872)
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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, 4E, Kiev 03127, Ukraine
Email:
ykoz@ukr.net
O. E. Kamenshchikova
Affiliation:
Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue, 4E, Kiev 03127, Ukraine
Email:
kamalev@gmail.com
Keywords:
Orlicz processes,
bounds for the increments,
approximation
Received by editor(s):
March 7, 2012
Published electronically:
July 24, 2014
Article copyright:
© Copyright 2014
American Mathematical Society
