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An approximation of \(L_{p}(\Omega )\) processes. (English. Russian original) Zbl 1246.60052
Theory Probab. Math. Stat. 83, 71-82 (2011); translation from Teor. Jmovirn. Mat. Stat. 83, 59-68 (2010).
Summary: 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 \( L_{q}[0,2\pi]\).

60G07 General theory of stochastic processes
41A25 Rate of convergence, degree of approximation
42A10 Trigonometric approximation
Full Text: DOI
[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) · Zbl 1026.60040
[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). · Zbl 1064.60058
[3] Olexandra Kamenschykova, Approximation of random processes by cubic splines, Theory Stoch. Process. 14 (2008), no. 3-4, 53 – 66. · Zbl 1224.65016
[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. · Zbl 0998.60503
[6] N. I. Achieser, Theory of approximation, Translated by Charles J. Hyman, Frederick Ungar Publishing Co., New York, 1956. · Zbl 0072.28403
[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). · Zbl 0955.60037
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