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Theory of Probability and Mathematical Statistics



Accuracy and reliability of a model of a Gaussian homogeneous and isotropic random field in the space C(T)

N. V. Troshki

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Abstract: In this paper we studied accuracy and reliability of a model of a homogeneous and isotropic random field in the space C(T).

Keywords: Gaussian random fields, homogeneous and isotropic field, simulation, accuracy and reliability.

Bibliography:
1. V. Buldygin, Yu. Kozachenko, Metric characterization of random variables and random processes, AMS, Providence, RI, 2000.
2. R. Guiliano Antonini, Yu. Kozachenko, T. Nikitina, Spaces of ?-sub-Gaussian random variables,Rend. Accad. Naz. Sci. XL Mem. Mat. Appl., 27 (2003), 95-124.
3. B. V. Dovhai, Yu. V. Kozachenko, H. I. Slyvka-Tylyshchak, The Boundary Value Problems of Mathematical Physics with Random Factors, Kiev University, 2008. (Ukrainian)
4. Yu. V. Kozachenko, L. F. Kozachenko, Simulation accuracy of stationary Gaussian stochastic processes in L2(0, T), J. Math. Sci., 72 (1994), no. 3, 3137-3143.
5. Yu. V. Kozachenko, A. O. Pashko, The accuracy of modeling random processes in norms of Orlicz spaces. I, Theory Probab. Math. Statist., 58 (2000), 51-66.
6. Yu. V. Kozachenko, A. O. Pashko, I. V. Rozora, Modeling of Random Processes and Fields, Zadruga, Kyiv, 2007. (Ukrainian)
7. Yu. V. Kozachenko, O. O. Pogoriliak, A. M. Tegza, Modelling of Gaussian Random Processes and Cox Processes, Karpaty, Uzhgorod, 2012. (Ukrainian)
8. Y. Kozachenko, O. Pogorilyak, I. Rozora, A. Tegza, Simulation of Stochastic Processes with Given Accuracy and Reliability, ISTE Press, London, Elsevier, Oxford, 2016.
9. Yu. V. Kozachenko, G. I. Slyvka, Justication of the Fourier method for hyperbolic equations with random initial conditions, Theory Probab. Math. Statist., 69 (2004), 67-83.
10. Y. Kozachenko, A. Slyvka-Tylyshchak, The Cauchy problem for the heat equation with a random right part from the space Sub?(?), Applied Mathematics, 5 (2014), 2318-2333.
11. Yu. V. Kozachenko, N. V. Troshki, Accuracy and reliability of a model of Gaussian random process in C(T) space, Int. J. Stat. Manag. Syst., 10 (2015), no. 12, 115.
12. G. A. Mikhailov, Modeling random processes and elds with the help of Palm processes, Doklady AN SSSR, 262 (1982), no. 3, 531-535. (Russian)
13. G. A. Mikhailov, Some Questions of the Theory of Monte Carlo Methods, Nauka, Novosibirsk, 1974. (Russian)
14. G. A. Mikhailov, K. K. Sabelfeld, On numerical simulation of impurity diusion in stochastic velocity elds, Izvestiya AN SSSR Ser. Physics, 16 (1980), no. 3, 229-235. (Russian)
15. G. A. Mikhailov, Approximate models of random processes and elds, Zh. Vychisl. Mat. i Mat.Fiz., 23 (1983), no. 3, 558-566. (Russian)
16. G. A. Mikhailov, A. V. Voytishek, Numerical Statistical Modeling, Akademia, Moscow, 2006. (Russian)
17. A. Olenko, T. Pogany Direct Lagrange-Yen type interpolation of random elds, Theory Stoch.Process., 9(25) (2003), no. 34, 242-254.
18. A. Olenko, T. Pogany On sharp Bbounds for remainders in multidimensional sampling theorem, Sampl. Theory Signal Image Process., 6 (2007), no. 3, 249-272.
19. N. V. Troshki, Upper bounds for supremums of the norms of the deviation between a homogeneous isotropic random eld and its model, Theor. Probab. Math. Statist., 94 (2017), 159-184.
20. N. V. Troshki, Accuracy and reliability of a model for a Gaussian homogeneous and isotropic random eld in the space Lp(T), p ? 1, Theory Probab. Math. Stat., 90 (2015), 183-200.
21. N. Troshki, Construction models of Gaussian random processes with a given accuracy and reliability in Lp(T), p ? 1, J. Classical Anal., 3 (2013), no. 2, 157-165.
22. Z. I. Vyzhva, On approximation of 3-D isotropic random elds on the sphere and statistical simulation, Theory Stoch. Process., 3 (1997), no. 34, 463-467.
23. M. I. Yadrenko, Spectral Theory of Random Fields, Optimization Software, Publications Division, New York, 1983.
24. M. I. Yadrenko, A. K. Rakhimov, Statistical simulation of a homogeneous isotropic random eld on the plane and estimations of simulation errors, Theory Probab. Math. Stat., 49 (1994), 177-181.