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

Published electronically:
February 2, 2012

MathSciNet review:
2768849

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Abstract | References | Similar Articles | Additional Information

Abstract: Bounds for the increments of stochastic processes belonging to some classes of the space are obtained in the metric. An approximation of such processes by trigonometric sums is studied in the space .

**1.**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).**3.**Olexandra Kamenschykova,*Approximation of random processes by cubic splines*, Theory Stoch. Process.**14**(2008), no. 3-4, 53–66. MR**2498604****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**, 10.1090/S0094-9000-09-00782-0**5.**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****6.**N. I. Achieser,*Theory of approximation*, Translated by Charles J. Hyman, Frederick Ungar Publishing Co., New York, 1956. MR**0095369****7.**Yu. V. Kozachenko,*Random processes in Orlicz function spaces*, Teor. Ĭmovīr. Mat. Stat.**60**(1999), 64–76 (Ukrainian, with Ukrainian summary); English transl., Theory Probab. Math. Statist.**60**(2000), 73–85 (2001). 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:
https://doi.org/10.1090/S0094-9000-2012-00842-9

Keywords:
The forward problem of harmonic approximation,
$L_{p}$ processes,
increments,
accuracy of approximation,
reliability of approximation

Received by editor(s):
June 10, 2010

Published electronically:
February 2, 2012

Article copyright:
© Copyright 2012
American Mathematical Society