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Accuracy and reliability of a model for a Gaussian homogeneous and isotropic random field in the space \(L_{p}(\mathbb{T})\), \(p\geq1\). (English. Ukrainian original) Zbl 1322.60070

Theory Probab. Math. Stat. 90, 183-200 (2015); translation from Teor. Jmovirn. Mat. Stat. 90, 161–176 (2014).
Summary: A model is constructed for a Gaussian homogeneous isotropic random field that approximates it with a given accuracy and reliability in the space \(L_p(T)\), \(p\geq 1\). The theory of the spaces \(\operatorname{Sub}(\Omega)\) is used for studying such a model.

MSC:

60G60 Random fields
60G15 Gaussian processes
60G07 General theory of stochastic processes
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[1] [E.M.] S. M. Ermakov and G. A. Mikha\u\ilov, A Course in Statistical Modeling, “Nauka”, Moscow, 1982. (Russian)
[2] [O.P.] V. A. Ogorodnikov and S. M. Prigarin, Numerical Modeling of Random Processes and Fields: Algorithms and Applications, VSP, Utrecht, 1996. · Zbl 0865.60002
[3] [K.S.V.] Yu. Kozachenko, T. Sottinen, and O. Vasylyk, Simulation of weakly self-similar stationary increment \(Sub_\varphi(\Omega)\)-processes: a series expansion approach, Methodology and Computing in Applied Probability 7 (2005), no. 3, 379-400. · Zbl 1082.60512
[4] [S.K.] K. K. Sabelfeld and O. A. Kurbanmuradov, Numerical statistical model of classical incompressible isotropic turbulence, Soviet Journal of Numerical Analysis and Mathematical Modeling 5 (1990), 251-263. · Zbl 0818.76032
[5] [K.P.R.] Yu. V. Kozachenko, A. O. Pashko, and I. V. Rozora, Modeling of Random Processes and Fields, “Zadruga”, Kyiv, 2007. (Ukrainian) · Zbl 1199.60003
[6] [T.F.] A. M. Tegza and N. V. Fedoryanych, Accuracy and reliability of a model of a Gaussian homogeneous and isotropic random field in the space \(C(T)\) with a bounded spectrum, Naukovyi Visnyk Uzhgorod University 22 (2011), no. 2, 142-147. (Ukrainian) · Zbl 1265.60084
[7] [K.R.] Yu. Kozachenko and I. Rozora, Simulation of Gaussian stochastic processes, Random Oper. Stoch. Equ. 11 (2003), no. 3, 275-296. · Zbl 1051.60040
[8] [K.R.T.] Yu. V. Kozachenko, I. V. Rozora, and Ye. V. Turchyn, On an expansion of random processes in series, Random Oper. Stoch. Equ. 15 (2007), no. 1, 15-33. · Zbl 1142.60349
[9] [K.T.] Yu. V. Kozachenko and A. M. Tegza, Application of the theory of \(Sub_\varphi(\Omega)\) spaces of random variables for determining the accuracy of the modeling of stationary Gaussian processes, Teor. Imovir. Mat. Stat. 67 (2002), 71-87; English transl. in Theory Probab. Math. Statist. 67 (2003), 79-96. · Zbl 1050.60045
[10] [T.] N. V. Troshki, Construction of models of Gaussian random fields with a given reliability and accuracy in \(L_p(\mathbbT), p\geq 1\), Appl. Stat. Actuarial and Finance Math. (2013), no. 1-2, 149-156. (Ukrainian)
[11] [K.P.] Yu. V. Kozachenko and O. O. Pogoriliak, Simulation of Cox processes driven by random Gaussian field, Methodology and Computing Appl. Probab. 13 (2011), no. 3, 511-521. · Zbl 1277.60088
[12] [K.M.1] Yu. V. Kozachenko and O. M. Moklyachuk, Stochastic processes in the spaces \(D_V,W\), Teor. Imovir. Mat. Stat. 82 (2010), 56-66; English transl. in Theory Probab. Math. Statist. 82 (2011), 43-56. · Zbl 1232.60030
[13] [K.M.2] Yu. V. Kozachenko and O. M. Moklyachuk, Sample continuity and modeling of stochastic processes from the spaces \(D_V,W\), Teor. Imovir. Mat. Stat. 83 (2010), 80-91; English transl. in Theory Probab. Math. Statist. 83 (2011), 95-110. · Zbl 1251.60030
[14] [K.Ml.] Yu. V. Kozachenko and Yu. Yu. Mlavets’, The Banach spaces \(F_\psi(\Omega)\) of random variables, Teor. Imovir. Mat. Stat. 86 (2012), 92-107; English transl. in Theory Probab. Math. Statist. 86 (2013), 105-121. · Zbl 1305.60025
[15] [B.K.] V. V. Buldygin and Yu. V. Kozachenko, Metric Characterization of Random Variables and Random Processes, “TViMS”, Kyiv, 1998; English transl., American Mathematical Society, Providence, RI, 2000. · Zbl 0933.60031
[16] [Ya.] M. I. Yadrenko, Spectral Theory of Random Fields, “Vyshcha shkola”, Kiev, 1980; English transl., Optimization Software, Inc., Publications Division, New York-Heidelberg-Berlin, 1983.
[17] [B.E.] H. Bateman and A. Erdelyi, Higher Transcendental Functions, vol. 2, McGraw-Hill, New York-Toronto-London, 1953. · Zbl 0143.29202
[18] [K.K.] Yu. V. Kozachenko and O. E. Kamenshchikova, Approximation of \(SSub_\varphi(\Omega)\) stochastic processes in the space \(L_p(\mathbbT)\), Teor. Imovir. Mat. Stat. 79 (2008), 73-78; English transl. in Theory Probab. Math. Statist. 79 (2009), 83-88. · Zbl 1224.60067
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