On a distribution of maximum of Gaussian field witha constant variance on a smooth manifold

Theory of Probability and its Applications

Volumn 41, Issue 2, 1996, Pages 367-379

  Mikhaleva, T L ^b   Piterbarg, V I ^a  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

^b NONE

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Indexed keywords

EID: 0030336732     PISSN: 0040585X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (11)

1. J. PICKANDS, III, Upcrossing probabilities for stationary Gaussian process, Trans. Amer. Math. Soc., 145 (1969), pp. 51-73.
2. V. I. PITERBARG, Asymptotic methods in the theory of random Gaussian processes and fields, Moscow State University, Moscow, 1988 (in Russian).
3. T. L. MIKHALEVA, Probabilities of large deviations of two-dimensional Gaussian processes with differently distributed independent components, Vestnik MGU, Ser. 1, 3 (1991), pp. 82-84 (in Russian).
4. V. PITERBARG AND YU. TYURIN, Homogeneity testing of two samples, Math. Methods Statist., 2 (1993), pp. 147-164.
5. 2-process and other functions of multidimensional Gaussian processes, with reliability applications, Adv. in Appl. Probab., 12 (1980), pp. 746-774.
6. 2-process and its concomitants, J. Multivariate Anal., 10 (1980), pp. 181-206.
7. 2-processes with dependent components with application to envelope upcrossings, J. Appl. Probab., 26 (1989), pp. 36-49.
8. V. PITERBARG, High deviations for multidimensional stationary Gaussian process with independent coordinates, University of Lund and Lund Institute of Technology, Department of Math. Statistics, Report 1991, 6.
9. YU. K. BELYAEV AND V. I. PITERBARG, The asymptotic behavior of the average number of the A-points of upcrossings of a Gaussian field beyond a high level, Dokl. Akad. Nauk SSSR. 203 (1972), pp. 9-12 (in Russian).
10. C. BORELL, The Brunn-Minkowski inequality in Gauss space, Invent. Math., 30 (1975), pp. 207-216.
11. D. SLEPIAN, The one-sided barrier problem for the Gaussian noise, Bell System Tech. J., 41 (1962), pp. 463-501.