Accuracy and reliability of a model for a Gaussian homogeneous and isotropic random field in the space 𝐿_{𝑝}(𝕋), 𝕡≥1

Troshki, N.

doi:10.1090/tpms/959

Accuracy and reliability of a model for a Gaussian homogeneous and isotropic random field in the space $L_p(\mathbb {T})$, $p\geq 1$

Author: N. V. Troshki
Translated by: N. Semenov
Journal: Theor. Probability and Math. Statist. 90 (2015), 183-200
MSC (2010): Primary 60G15; Secondary 60G07
DOI: https://doi.org/10.1090/tpms/959
Published electronically: August 11, 2015
MathSciNet review: 3242030
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: 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.

References

S. M. Ermakov and G. A. Mikhaĭlov, Statisticheskoe modelirovanie, 2nd ed., “Nauka”, Moscow, 1982 (Russian). MR 705787
V. A. Ogorodnikov and S. M. Prigarin, Numerical modelling of random processes and fields, VSP, Utrecht, 1996. Algorithms and applications. MR 1419502
Yuriy Kozachenko, Tommi Sottinen, and Olga Vasylyk, Simulation of weakly self-similar stationary increment ${\rm Sub}_\phi (\Omega )$-processes: a series expansion approach, Methodol. Comput. Appl. Probab. 7 (2005), no. 3, 379–400. MR 2210587, DOI https://doi.org/10.1007/s11009-005-4523-y
K. K. Sabel′fel′d and O. A. Kurbanmuradov, Numerical statistical model of classical incompressible isotropic turbulence, Soviet J. Numer. Anal. Math. Modelling 5 (1990), no. 3, 251–263. MR 1122132

Yu. V. Kozachenko, A. O. Pashko, and I. V. Rozora, Modeling of Random Processes and Fields, “Zadruga”, Kyiv, 2007. (Ukrainian)

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)

Yuri Kozachenko and Iryna Rozora, Simulation of Gaussian stochastic processes, Random Oper. Stochastic Equations 11 (2003), no. 3, 275–296. MR 2009187, DOI https://doi.org/10.1163/156939703771378626

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. MR 2316186, DOI https://doi.org/10.1515/ROSE.2007.002

Yu. V. Kozachenko and A. M. Tegza, Application of the theory of ${\rm Sub}_\phi (\Omega )$ spaces of random variables for determining the accuracy of the modeling of stationary Gaussian processes, Teor. Ĭmovīr. Mat. Stat. 67 (2002), 71–87 (Ukrainian, with Ukrainian summary); English transl., Theory Probab. Math. Statist. 67 (2003), 79–96. MR 1956621

N. V. Troshki, Construction of models of Gaussian random fields with a given reliability and accuracy in $L_p(\mathbb {T})$, $p\geq 1$, Appl. Stat. Actuarial and Finance Math. (2013), no. 1–2, 149–156. (Ukrainian)

Yurij Kozachenko and Oleksandr Pogoriliak, Simulation of Cox processes driven by random Gaussian field, Methodol. Comput. Appl. Probab. 13 (2011), no. 3, 511–521. MR 2822393, DOI https://doi.org/10.1007/s11009-010-9169-8

Yu. V. Kozachenko and O. M. Moklyachuk, Random processes in the spaces $D_{V,W}$, Teor. Ĭmovīr. Mat. Stat. 82 (2010), 56–66 (Ukrainian, with English, Russian and Ukrainian summaries); English transl., Theory Probab. Math. Statist. 82 (2011), 43–56. MR 2790483, DOI https://doi.org/10.1090/S0094-9000-2011-00826-5

Yu. V. Kozachenko and O. M. Moklyachuk, Selective continuity and modeling of random processes from the spaces $D_{V,W}$, Teor. Ĭmovīr. Mat. Stat. 83 (2010), 80–91 (Ukrainian, with English, Russian and Ukrainian summaries); English transl., Theory Probab. Math. Statist. 83 (2011), 95–110. MR 2768851, DOI https://doi.org/10.1090/S0094-9000-2012-00844-2

Yu. V. Kozachenko and Yu. Yu. Mlavets′, The Banach spaces of ${\bf F}_\psi (\Omega )$ of random variables, Teor. Ĭmovīr. Mat. Stat. 86 (2011), 92–107 (Ukrainian, with English, Russian and Ukrainian summaries); English transl., Theory Probab. Math. Statist. 86 (2013), 105–121. MR 2986453, DOI https://doi.org/10.1090/S0094-9000-2013-00892-8

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

M. Ĭ. Jadrenko, Spektral′naya teoriya sluchaĭ nykh poleĭ, “Vishcha Shkola”, Kiev, 1980 (Russian). MR 590889

Arthur Erdélyi, Wilhelm Magnus, Fritz Oberhettinger, and Francesco G. Tricomi, Higher transcendental functions. Vols. I, II, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1953. Based, in part, on notes left by Harry Bateman. MR 0058756

Yu. V. Kozachenko and O. Ē. Kamenshchikova, Approximation of ${\rm SSub}_\phi (\Omega )$ random processes in the space $L_p(\Bbb T)$, Teor. Ĭmovīr. Mat. Stat. 79 (2008), 73–78 (Ukrainian, with Ukrainian summary); English transl., Theory Probab. Math. Statist. 79 (2009), 83–88. MR 2494537, DOI https://doi.org/10.1090/S0094-9000-09-00782-0