Extremes of the standardized Gaussian noise

Stochastic Processes and their Applications

Volumn 121, Issue 3, 2011, Pages 515-533

  Kabluchko, Zakhar ^a  

^a UNIVERSITY OF ULM   (Germany)

Author keywords

Extremes; Gaussian fields; Gumbel distribution; Local self similarity; Pickands' double sum method; Poisson clumping heuristics; Scan statistics

Indexed keywords

EXTREMES; GAUSSIAN FIELD; GUMBEL DISTRIBUTION; LOCAL SELFSIMILARITY; PICKANDS' DOUBLE-SUM METHOD; POISSON CLUMPING HEURISTICS; SCAN STATISTICS;

GAUSSIAN DISTRIBUTION; GAUSSIAN NOISE (ELECTRONIC); OPTICAL COMMUNICATION; RANDOM VARIABLES;

POISSON DISTRIBUTION;

EID: 78751575600     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spa.2010.11.007     Document Type: Article

References (26)

1. P. Albin On extremal theory for stationary processes Ann. Probab. 18 1 1990 92 128
2. D. Aldous Probability approximations via the Poisson clumping heuristic Applied Mathematical Sciences vol. 77 1989 Springer-Verlag New York
3. R. Arratia, L. Goldstein, and L. Gordon Two moments suffice for Poisson approximations: The ChenStein method Ann. Probab. 17 1 1989 9 25
4. S.M. Berman Maxima and high level excursions of stationary Gaussian processes Trans. Amer. Math. Soc. 160 1971 65 85
5. S.M. Berman A class of limiting distributions of high level excursions of Gaussian processes Z. Wahrscheinlichkeitstheor. Verw. Geb. 21 1972 121 134
6. S.M. Berman Sojourns and extremes of Gaussian processes Ann. Probab. 2 1974 999 1026
7. S.M. Berman Sojourns and extremes of stochastic processes Wadsworth & Brooks/Cole Statistics/Probability Series 1992
8. P. Bickel, and M. Rosenblatt Two-dimensional random fields Multivariate analysis, III (Proc. Third Internat. Sympos., Wright State Univ., Dayton, Ohio, 1972) 1973 Academic Press New York 3 15
9. H.P. Chan, and T.L. Lai Maxima of asymptotically Gaussian random fields and moderate deviation approximations to boundary crossing probabilities of sums of random variables with multidimensional indices Ann. Probab. 34 1 2006 80 121
10. J. Hsler Extreme values and high boundary crossings of locally stationary Gaussian processes Ann. Probab. 18 3 1990 1141 1158
11. Z. Kabluchko, Extreme-value analysis of standardized Gaussian increments. Unpublished preprint. Available at http://www.arxiv.org/abs/0706.1849, 2007.
12. Z. Kabluchko, and A. Munk Exact convergence rate for the maximum of standardized Gaussian increments Electron. Comm. Probab. 13 2008 302 310
13. Z. Kabluchko, and A. Munk Shao's theorem on the maximum of standardized random walk increments for multidimensional arrays ESAIM Probab. Stat. 13 2009 409 416
14. M.R. Leadbetter, G. Lindgren, and H. Rootzn Extremes and related properties of random sequences and processes Springer Series in Statistics 1983 Springer-Verlag New York
15. T.L. Mikhaleva, and V.I. Piterbarg On the distribution of the maximum of a Gaussian field with a constant variance on a smooth manifold Theory Probab. Appl. 41 2 1996 367 379
16. T. Mikosch, and A. Rakauskas The limit distribution of the maximum increment of a heavy-tailed random walk Bernoulli 16 4 2010 1016 1038
17. J. Pickands Upcrossing probabilities for stationary Gaussian processes Trans. Amer. Math. Soc. 145 1969 51 73
18. J. Pickands Asymptotic properties of the maximum in a stationary Gaussian process Trans. Amer. Math. Soc. 145 1969 75 86
19. V.I. Piterbarg Asymptotic methods in the theory of Gaussian processes and fields Translations of Mathematical Monographs vol. 148 1996 American Mathematical Society Providence, RI
20. V.I. Piterbarg, and V.R. Fatalov The Laplace method for probability measures in Banach spaces Russian Math. Surveys 50 6 1995 1151 1239
21. C. Qualls, and H. Watanabe Asymptotic properties of Gaussian processes Ann. Math. Statist. 43 1972 580 596
22. C. Qualls, and H. Watanabe Asymptotic properties of Gaussian random fields Trans. Amer. Math. Soc. 177 1973 155 171
23. Q.-M. Shao On a conjecture of Rvsz Proc. Amer. Math. Soc. 123 2 1995 575 582
24. D. Siegmund, and E.S. Venkatraman Using the generalized likelihood ratio statistic for sequential detection of a change-point Ann. Statist. 23 1 1995 255 271
25. D. Siegmund, and B. Yakir Tail probabilities for the null distribution of scanning statistics Bernoulli 6 2 2000 191 213
26. J. Steinebach On a conjecture of Rvsz and its analogue for renewal processes B. Szyszkowicz, Asymptotic Methods in Probability and Statistics, A volume in honour of Mikls Csrg. ICAMPS'97 1998 North-Holland/Elsevier