An approximation of $L_p(\Omega )$ processes
Authors:
O. E. Kamenshchikova and T. O. Yanevich
Translated by:
O. Klesov
Journal:
Theor. Probability and Math. Statist. 83 (2011), 71-82
MSC (2010):
Primary 60G07, 41A25; Secondary 42A10
DOI:
https://doi.org/10.1090/S0094-9000-2012-00842-9
Published electronically:
February 2, 2012
MathSciNet review:
2768849
Full-text PDF Free Access
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Additional Information
Abstract: Bounds for the increments of stochastic processes belonging to some classes of the space $L_p(\Omega )$ are obtained in the $L_q[a,b]$ metric. An approximation of such processes by trigonometric sums is studied in the space $L_{q}[0,2\pi ]$.
References
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- T. O. Yakovenko, Properties of increments of processes belonging to Orlicz spaces, Visnyk Kyiv University, Ser. Matematika, Mekhanika (2003), no. 9โ10, 142โ147. (Ukrainian).
- Olexandra Kamenschykova, Approximation of random processes by cubic splines, Theory Stoch. Process. 14 (2008), no. 3-4, 53โ66. MR 2498604
- Yu. V. Kozachenko and O. ฤ. Kamenshchikova, Approximation of ${\rm SSub}_\phi (\Omega )$ random processes in the space $L_p(\Bbb T)$, Teor. ฤฌmovฤซr. Mat. Stat. 79 (2008), 73โ78 (Ukrainian, with Ukrainian summary); English transl., Theory Probab. Math. Statist. 79 (2009), 83โ88. MR 2494537, DOI https://doi.org/10.1090/S0094-9000-09-00782-0
- 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
- Yu. V. Kozachenko, Random processes in Orlicz function spaces, Teor. ฤฌmovฤซr. Mat. Stat. 60 (1999), 64โ76 (Ukrainian, with Ukrainian summary); English transl., Theory Probab. Math. Statist. 60 (2000), 73โ85 (2001). MR 1826143
References
- T. O. Yakovenko, Conditions for the belonging of stochastic processes to some Orlicz spaces of functions, Visnyk Kyiv University, Ser. fiz-mat. nauk (2002), no. 5, 64โ74. (Ukrainian)
- T. O. Yakovenko, Properties of increments of processes belonging to Orlicz spaces, Visnyk Kyiv University, Ser. Matematika, Mekhanika (2003), no. 9โ10, 142โ147. (Ukrainian).
- O. Kamenshchykova, Approximation of random processes by cubic splines, Theory Stoch. Processes 14(30) (2008), no. 3โ4, 53โ66. MR 2498604 (2010h:65007)
- Yu. V. Kozachenko and O. E. Kamenshchikova, Approximation of $\operatorname {SSub}_{\varphi }(\Omega )$ stochastic processes in the space $L_{p}(\mathbb {T})$, Teor. Imovirnost. ta Mat. Statist. 79 (2008), 73โ78; English transl. in Theor. Probability and Math. Statist. 79 (2009), 83โ88. MR 2494537 (2010d:60097)
- 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)
- N. I. Akhiezer [Achieser], Theory of Approximation, Nauka, Moscow, 1965; English transl. of the 1st edition: Frederick Ungar Publishing, New York, 1956. MR 0095369 (20:1872)
- Yu. V. Kozachenko, Stochastic processes in Orlicz function spaces, Teor. Imovirnost. i Mat. Statist. 60 (1999), 64โ76; English transl. in Theor. Probability and Math. Statist. 60 (2000), 73โ85. MR 1826143
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Additional Information
O. E. Kamenshchikova
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:
kamalev@gmail.com
T. O. Yanevich
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:
yata452@univ.kiev.ua
Keywords:
The forward problem of harmonic approximation,
$L_p$ processes,
increments,
accuracy of approximation,
reliability of approximation
Received by editor(s):
June 10, 2010
Published electronically:
February 2, 2012
Article copyright:
© Copyright 2012
American Mathematical Society
