Theory of Probability and Mathematical Statistics
Accuracy and reliability of a model for a Gaussian homogeneous and isotropic random field in the space Lp(T), p≥1
N. V. Troshki
Download PDF
Abstract: A model is constructed for a Gaussian homogeneous isotropic random field that approximates it with a given accuracy and reliability in the space Lp(T), p≥1. The theory of the spaces Sub(Ω) is used for studying such a model.
Keywords: Gaussian random fields, homogeneous and isotropic fields, models of random fields, accuracy and reliability
Bibliography: 1. S. M. Ermakov and G. A. Mikhaĭlov, A Course in Statistical Modeling, ''Nauka'', Moscow, 1982. (Russian)
2. V. A. Ogorodnikov and S. M. Prigarin, Numerical Modeling of Random Processes and Fields: Algorithms and Applications, VSP, Utrecht, 1996.
3. Yu. Kozachenko, T. Sottinen, and O. Vasylyk, Simulation of weakly self-similar stationary increment Sub_φ(Ω)-processes: a series expansion approach, Methodology and Computing in Applied Probability 7 (2005), no. 3, 379-400.
4. 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.
5. Yu. V. Kozachenko, A. O. Pashko, and I. V. Rozora, Modeling of Random Processes and Fields, ''Zadruga'', Kyiv, 2007. (Ukrainian)
6. 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)
7. Yu. Kozachenko and I. Rozora, Simulation of Gaussian stochastic processes, Random Oper. Stoch. Equ. 11 (2003), no. 3, 275-296.
8. 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.
9. Yu. V. Kozachenko and A. M. Tegza, Application of the theory of Sub_φ(Ω) 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.
10. N. V. Troshki, Construction of models of Gaussian random fields with a given reliability and accuracy in Lp(T), p≥1, Appl. Stat. Actuarial and Finance Math. (2013), no. 1-2, 149-156. (Ukrainian)
11. 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.
12. 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.
13. 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.
14. Yu. V. Kozachenko and Yu. Yu. Mlavets', The Banach spaces Fψ(Ω) of random variables, Teor. Imovir. Mat. Stat. 86 (2012), 92-107; English transl. in Theory Probab. Math. Statist. 86 (2013), 105-121.
15. 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.
16. 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. H. Bateman and A. Erdelyi, Higher Transcendental Functions, vol. 2, McGraw-Hill, New York-Toronto-London, 1953.
18. Yu. V. Kozachenko and O. E. Kamenshchikova, Approximation of SSub_φ(Ω) stochastic processes in the space Lp(T), Teor. Imovir. Mat. Stat. 79 (2008), 73-78; English transl. in Theory Probab. Math. Statist. 79 (2009), 83-88.
