On Proximity of Correlation Functions of Homogeneous and Isotropic Random Fields Whose Spectral Functions Coincide on a Certain Set
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We give examples of application of the mean-value theorem to finding various estimates of the proximity of correlation functions in the case where their spectral functions coincide on a certain set.
KeywordsCorrelation Function Random Field Spectral Function Isotropic Random Field Isotropic Random
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- 1.V. M. Zolotarev, Contemporary Theory of Summation of Independent Random Variables [in Russian], Nauka, Moscow (1986).Google Scholar
- 2.M. I. Yadrenko, Spectral Theory of Random Fields [in Russian], Vyshcha Shkola, Kiev (1980).Google Scholar
- 3.G. N. Watson, A Treatise on the Theory of Bessel Functions Cambridge University Press, Cambridge (1944).Google Scholar
- 4.A. Ya. Dorogovtsev, Mathematical Analysis [in Russian], Vyshcha Shkola, Kiev (1985).Google Scholar
- 5.D. V. Pavlov, “Some relations for probability metrics for random fields,” Visn. Kiev Univ., Ser. Fiz.-Mat. Nauk Issue 2, 135–141 (1999).Google Scholar
- 6.A. Ya. Olenko, “On proximity of the spectral functions of homogeneous isotropic fields,” Theory Probab. Math. Stat. 46, 117–119 (1993).Google Scholar
- 7.A. Ya. Olenko, “On the properties of spectral and correlation functions,” in: Proc. of the 4th World Congr. Bernoulli Soc. Vienna (1996), pp. 363–364.Google Scholar
- 8.A. Ya. Olenko and D. V. Pavlov, “Some estimates for the proximity of correlation and spectral functions of random fields,” Nauk. Zap. Univ. “Kievo-Mogilyanskaya Akademiya”, Ser. Fiz.-Mat. Nauk 18, 17–19 (2000).Google Scholar