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Spherical level-crossing measures for chi-square random fields. (English. Russian original) Zbl 0835.60043

J. Math. Sci., New York 69, No. 6, 1463-1471 (1994); translation from Vychisl. Prikl. Mat., Kiev 68, 118-128 (1989).
See the review in Zbl 0716.60051.

MSC:

60G60 Random fields

Citations:

Zbl 0716.60051
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Full Text: DOI

References:

[1] I. N. Kovalenko and O. V. Sarmanov, A Short Course in the Theory of Stochastic Processes [in Russian], Kiev (1978).
[2] N. N. Leonenko, ”On level crossing measures of a Gaussian isotropic field,” Teor. Veroyat. Mat. Stat., No. 31, 64-82 (1984).
[3] N. N. Leonenko and A. V. Ivanov, Statistical Analysis of Random Fields [in Russian], Kiev (1986). · Zbl 0721.62097
[4] N. N. Leonenko and A. Kh. El’-Bassionii, ”Limit theorems for some level crossing characteristics,” Teor. Veroyat. Mat. Stat., No. 35, 55-60 (1986).
[5] O. V. Sarmanov, ”Analysis of stationary Markov processes using eigenfunction expansions,” Tr. Mat. Inst. Akad. Nauk SSSR,60, 238-261 (1961). · Zbl 0229.60051
[6] M. I. Yadrenko, Spectral Theory of Random Fields [in Russian], Kiev (1980). · Zbl 0441.60055
[7] S. M. Berman, ”High level sojourns for strongly dependent Gaussian processes,” Z. Wahrsch. verw. Geb.,50, 223-236 (1979). · Zbl 0421.60033 · doi:10.1007/BF00533641
[8] S. M. Berman, ”Sojourns of vector Gaussian processes inside and outside spheres,” Z. Wahrsch. verw. Geb.,66, 529-542 (1984). · Zbl 0561.60042 · doi:10.1007/BF00531889
[9] M. Maejima, ”Some sojourn time problems for strongly dependent processes,” Z. Wahrsch. verw. Geb.,57, 1-14 (1981). · Zbl 0446.60021 · doi:10.1007/BF00533711
[10] P. Major, ”Multiple Wiener?Ito integrals,” Lect. Notes Math., vol. 849 (1981). · Zbl 0451.60002
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