Upper bounds for supremums of the norms of the deviation between a homogeneous isotropic random field and its model
Author:
N. V. Troshki
Translated by:
N. Semenov
Journal:
Theor. Probability and Math. Statist. 94 (2017), 159-184
MSC (2010):
Primary 60G15; Secondary 60G07
DOI:
https://doi.org/10.1090/tpms/1016
Published electronically:
August 25, 2017
MathSciNet review:
3553461
Full-text PDF
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Abstract: Some estimates are obtained for the norm of the deviation between a homogeneous isotropic random field and its model.
References
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- R. Giuliano Antonini, Yu. Kozachenko, and T. Nikitina, Spaces of $\phi $-sub-Gaussian random variables, Rend. Accad. Naz. Sci. XL Mem. Mat. Appl. (5) 27 (2003), 95–124 (English, with English and Italian summaries). MR 2056414
- Yu. V. Kozachenko and L. F. Kozachenko, On the accuracy of modeling stationary Gaussian random processes in $L^2(0,T)$, Vychisl. Prikl. Mat. (Kiev) 75 (1991), 108–115 (Russian); English transl., J. Math. Sci. 72 (1994), no. 3, 3137–3143. MR 1168858, DOI https://doi.org/10.1007/BF01259486
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- Yu. V. Kozachenko, A. O. Pashko, and I. V. Rozora, Modeling Random Processes and Fields, “Zadruga”, Kyiv, 2007. (Ukrainian)
- Yu. V. Kozachenko, O. O. Pogorilyak, and A. M. Tegza, Modeling Gaussian Random Processes and Cox Processes, “Karpaty”, Uzhgorod, 2012. (Ukrainian)
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- G. A. Mikhaĭlov and A. V. Voĭtishek, Numerical statistical modeling, “Akademia”, Moscow, 2006. (Russian)
- N. V. Troshkī, Accuracy and reliability of a model of a Gaussian homogeneous and isotropic random field in the space $L_p(\Bbb T)$, $p\ge 1$, Teor. Ĭmovīr. Mat. Stat. 90 (2014), 161–176 (Ukrainian, with English, Russian and Ukrainian summaries); English transl., Theory Probab. Math. Statist. 90 (2015), 183–200. MR 3242030, DOI https://doi.org/10.1090/S0094-9000-2015-00959-5
- Nataliya Troshki, Construction models of Gaussian random processes with a given accuracy and reliability in $L_p(T)$, $p\geqslant 1$, J. Class. Anal. 3 (2013), no. 2, 157–165. MR 3322266, DOI https://doi.org/10.7153/jca-03-14
- Z. O. Vyzhva, On approximation of 3-D isotropic random fields on the sphere and statistical simulation, Theory Stoch. Process. 3 (1997), no. 3–4, 463–467.
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- M. I. Yadrenko and A. K. Rakhimov, Statistical simulation of a homogeneous isotropic random field on the plane and estimations of simulation errors, Teor. Ĭmovīr. Mat. Stat. 49 (1993), 245–251 (Ukrainian, with Ukrainian summary); English transl., Theory Probab. Math. Statist. 49 (1994), 177–181 (1995). MR 1445264
References
- V. V. Buldygin and Yu. V. Kozachenko, Metric Characterization of Random Variables and Random Processes, “TBiMS”, Kiev, 1998; English transl., American Mathematical Society, Providence, RI, 2000. MR 1743716
- R. Guiliano Antonini, Yu. Kozachenko, and T. Nikitina, Spaces of $\varphi$-subgaussian random variables, Memorie di Matematica e Applicazioni XXVII (1) (2003), 95–124. MR 2056414
- Yu. V. Kozachenko and L. F. Kozachenko, Modeling accuracy in $L_2(0,T)$ of Gaussian stochastic processes, Vychisl. Prikl. Mat. 75 (1991), 108–115. (Russian) MR 1168858
- Yu. V. Kozachenko and A. O. Pashko, The accuracy of modeling random processes in norms of Orlicz spaces. I, Teor. Ĭmovir. Mat. Stat. 58 (1988), 45–60; English transl. in Theory Probab. Math. Statist. 58 (1999), 51–66. MR 1793641
- Yu. V. Kozachenko, A. O. Pashko, and I. V. Rozora, Modeling Random Processes and Fields, “Zadruga”, Kyiv, 2007. (Ukrainian)
- Yu. V. Kozachenko, O. O. Pogorilyak, and A. M. Tegza, Modeling Gaussian Random Processes and Cox Processes, “Karpaty”, Uzhgorod, 2012. (Ukrainian)
- Yu. Kozachenko and A. Slyvka-Tylyshchak, The Cauchy problem for the heat equation with a random right part of the space $\mathrm {Sub}_{\varphi }(\Omega )$, Appl. Math. 5 (2014), 2318–2333.
- Yu. V. Kozachenko and N. V. Troshki, Accuracy and reliability of a model of a Gaussian random process in $C(\mathbb {T})$ space, Inter. J. Statist. Management System 10 (2015), no. 1–2, 1–15.
- G. A. Mikhaĭlov, Modeling random processes and fields with the help of Palm processes, Doklady AN SSSR 262 (1982), no. 3, 531–535. (Russian)
- G. A. Mikhaĭlov, Some questions on the theory of Monte Carlo methods, “Nauka”, Novosibirsk, 1974. (Russian) MR 0405785
- G. A. Mikhaĭlov and K. K. Sabel’fel’d, On numerical simulation of impurity diffusion in stochastic velocity fields, Izvestiya AN SSSR Ser. Physics 16 (1980), no. 3, 229–235. (Russian)
- G. A. Mikhaĭlov, Approximate models of stochastic processes and fields, Zh. Vychisl. Matem. Matem. Fiz. 23 (1983), no. 3, 558–566; English transl. in USSR Comput. Math. Math. Physics 23 (1983), no. 3, 28–33. MR 706881
- G. A. Mikhaĭlov and A. V. Voĭtishek, Numerical statistical modeling, “Akademia”, Moscow, 2006. (Russian)
- N. V. Troshki, Accuracy and reliability of a model for a Gaussian homogeneous and isotropic random field in the space $L_p(\mathbb {T})$, $p\geq 1$ Teor. Ĭmovirnost. Matem. Statyst. 90 (2014), 161–176; English transl. in Theor. Probability and Math. Statist. 90 (2015), 183–200. MR 3242030
- N. Troshki, Construction models of Gaussian random processes with a given accuracy and reliability in $L_p(\mathbb {T})$, $p\geq 1$, J. Classical Anal. 3 (2013), no. 2, 157–165. MR 3322266
- Z. O. Vyzhva, On approximation of 3-D isotropic random fields on the sphere and statistical simulation, Theory Stoch. Process. 3 (1997), no. 3–4, 463–467.
- M. I. Yadrenko, Spectral Theory of Random Fields, “Vyshcha Shkola”, Kiev, 1980; English transl., Optimization Software, Inc., New York, 1983. MR 590889
- M. I. Yadrenko and G. K. Rakhimov, Statistical simulation of a homogeneous and isotropic field on the plane and estimations of simulation errors, Teor. Ĭmovirnost. Matem. Statyst. 49 (1993), 245–251; English transl. in Theor. Probability and Math. Statist. 49 (1994), 177–181. MR 1445264
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Additional Information
N. V. Troshki
Affiliation:
Department of Probability Theory and Mathematical Analysis, Uzhgorod National University, Universytets’ka Street, 14, Uzhgorod 88000, Ukraine
Email:
FedoryanichNatali@ukr.net
Keywords:
Gaussian random fields,
homogeneous and isotropic fields,
modeling,
accuracy and reliability
Received by editor(s):
April 20, 2016
Published electronically:
August 25, 2017
Article copyright:
© Copyright 2017
American Mathematical Society
