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An approximation of  processes
Authors:
O. E. Kamenshchikova and T. O. Yanevich
Translated by:
O. Klesov
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom 83 (2010).
Journal:
Theor. Probability and Math. Statist. 83 (2011), 71-82
MSC (2010):
Primary 60G07, 41A25; Secondary 42A10
Posted:
February 2, 2012
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Additional Information
Abstract: Bounds for the increments of stochastic processes belonging to some classes of the space  are obtained in the ![$ L_q[a,b]$](images/img3.gif) metric. An approximation of such processes by trigonometric sums is studied in the space ![$ L_{q}[0,2\pi ]$](images/img4.gif) .
References
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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, 64-74. (Ukrainian)
- 2.
T. O. Yakovenko, Properties of increments of processes belonging to Orlicz spaces, Visnyk Kyiv University, Ser. Matematika, Mekhanika (2003), no. 9-10, 142-147. (Ukrainian).
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O. Kamenshchykova, Approximation of random processes by cubic splines, Theory Stoch. Processes 14(30) (2008), no. 3-4, 53-66. MR 2498604 (2010h:65007)
- 4.
Yu. V. Kozachenko and O. Ē. Kamenshchikova, Approximation of
𝑆𝑆𝑢𝑏ᵩ(Ω) random processes in
the space 𝐿_{𝑝}(𝕋), Teor.
Ĭmovīr. Mat. Stat. 79 (2008), 73–78
(Ukrainian, with Ukrainian summary); English transl., Theory Probab. Math. Statist. 79 (2009), 83–88. MR 2494537
(2010d:60097), http://dx.doi.org/10.1090/S0094-9000-09-00782-0
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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)
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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)
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Yu. V. Kozachenko, Stochastic processes in Orlicz function spaces, Teor. Imovirnost. i Mat. Statist. 60 (1999), 64-76; English transl. in Theor. Probability and Math. Statist. 60 (2000), 73-85. 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
DOI:
http://dx.doi.org/10.1090/S0094-9000-2012-00842-9
PII:
S 0094-9000(2012)00842-9
Keywords:
The forward problem of harmonic approximation,
$L_{p}$ processes,
increments,
accuracy of approximation,
reliability of approximation
Received by editor(s):
10/JUN/2010
Posted:
February 2, 2012
Article copyright:
© Copyright 2012 American Mathematical Society
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