Geodesic
Limit theorem for high level $a$-upcrossings
Teoriâ veroâtnostej i ee primeneniâ, Tome 48 (2003) no. 4, pp. 811-818 Cet article a éte moissonné depuis la source Math-Net.Ru

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This paper proves the Poisson limit theorem for a number of large excursions of the modulus of the Gaussian vector process with independent identically distributed increments.
Keywords: Gaussian process, $\chi$-square process.
Mots-clés : large excursion 
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V. I. Piterbarg; S. Stamatović. Limit theorem for high level $a$-upcrossings. Teoriâ veroâtnostej i ee primeneniâ, Tome 48 (2003) no. 4, pp. 811-818. http://geodesic.mathdoc.fr/item/TVP_2003_48_4_a10/

[1] Adler R. J., “On excursion sets, tube formulas and maxima of random fields”, Ann. Appl. Probab., 10:1 (2000), 1–74 | MR | Zbl

[2] Kramer G., Lidbetter M., Statsionarnye sluchainye protsessy, Mir, M., 1969, 398 pp.

[3] Illsley R., “The excursions of a stationary Gaussian process outside a large two-dimensional region”, Adv. Appl. Probab., 33 (2001), 141–159 | DOI | MR | Zbl

[4] Kallenberg O., Random Measures, Akademie-Verlag, Berlin; Academic Press, London, 1983, 187 pp. | MR

[5] Lidbetter M., Lindgren G., Rotsen Kh., Ekstremumy sluchainykh posledovatelnostei i protsessov, Mir, M., 1989, 187 pp. | MR

[6] Piterbarg V. I., Asymptotic Methods in the Theory of Gaussian Processes and Fields, AMS, Providence, 1996, 296 pp. | MR | Zbl

[7] Rusakov A. A., Puassonovost raspredeleniya chisla vykhodov za vysokii uroven ogibayuschei gaussovskogo statsionarnogo protsessa, Deponirovano VINITI, 28.10.01 No 2142-B2001, 23 pp.