Geodesic
A functional central limit theorem for the measure of level surfaces of a Gaussian random field
Teoriâ veroâtnostej i ee primeneniâ, Tome 57 (2012) no. 1, pp. 168-178 
D. Meschenmoser; A. P. Shashkin. A functional central limit theorem for the measure of level surfaces of a Gaussian random field. Teoriâ veroâtnostej i ee primeneniâ, Tome 57 (2012) no. 1, pp. 168-178. http://geodesic.mathdoc.fr/item/TVP_2012_57_1_a8/
@article{TVP_2012_57_1_a8,
     author = {D. Meschenmoser and A. P. Shashkin},
     title = {A functional central limit theorem for the measure of level surfaces of a {Gaussian} random field},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {168--178},
     year = {2012},
     volume = {57},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2012_57_1_a8/}
}
TY  - JOUR
AU  - D. Meschenmoser
AU  - A. P. Shashkin
TI  - A functional central limit theorem for the measure of level surfaces of a Gaussian random field
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 2012
SP  - 168
EP  - 178
VL  - 57
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TVP_2012_57_1_a8/
LA  - ru
ID  - TVP_2012_57_1_a8
ER  - 
%0 Journal Article
%A D. Meschenmoser
%A A. P. Shashkin
%T A functional central limit theorem for the measure of level surfaces of a Gaussian random field
%J Teoriâ veroâtnostej i ee primeneniâ
%D 2012
%P 168-178
%V 57
%N 1
%U http://geodesic.mathdoc.fr/item/TVP_2012_57_1_a8/
%G ru
%F TVP_2012_57_1_a8

Voir la notice de l'article provenant de la source Math-Net.Ru

[1] Bulinskii A. V., Shashkin A. P., Predelnye teoremy dlya assotsiirovannykh sluchainykh polei i rodstvennykh sistem, FIZMATLIT, M., 2008, 477 pp.

[2] Kramer G., Matematicheskie metody statistiki, Mir, M., 1975, 648 pp. | MR

[3] Leonenko N. N., Ivanov A. V., Statisticheskii analiz sluchainykh polei, Vischa shkola, Kiev, 1986, 216 pp. | MR | Zbl

[4] Prokhorov Yu. V., “Skhodimost sluchainykh protsessov i predelnye teoremy teorii veroyatnostei”, Teoriya veroyatn. i ee primen., 1:2 (1956), 177–238 | Zbl

[5] Federer G., Geometricheskaya teoriya mery, Nauka, M., 1987, 760 pp. | MR | Zbl

[6] Adler R. J., “Excursions above a fixed level by $n$-dimensional random fields”, J. Appl. Probab., 13 (1976), 276–289 | DOI | MR | Zbl

[7] Adler R. J., Taylor J. E., Random Fields and Geometry, Springer, New York, 2007, 448 pp. | MR

[8] Arcones M., “Limit theorems for nonlinear functionals of a stationary Gaussian sequence of vectors”, Ann. Probab., 22:4 (1994), 2242–2274 | DOI | MR | Zbl

[9] Azaïs J.-M., Wschebor M., Level Sets and Extrema of Random Processes and Fields, Wiley, Hoboken, 2009, 393 pp. | MR | Zbl

[10] Bulinski A., Spodarev E., Timmerman F., “Central limit theorems for the excursion set volumes of weakly dependent random fields”, Bernoulli, 18:1 (2012), 100–118 ; arXiv: 1005.0483v1 | DOI | Zbl

[11] Iribarren I., “Asymptotic behaviour of the integral of a function on the level set of a mixing random field”, Probab. Math. Statist., 10:1 (1989), 45–56 | MR | Zbl

[12] Kratz M. F., “Level crossings and other level functionals of stationary Gaussian processes”, Probab. Surv., 3 (2006), 230–288 | DOI | MR | Zbl

[13] Kratz M. F., León J. R., “Central limit theorems for level functionals of stationary Gaussian processes and fields”, J. Theoret. Probab., 14:3 (2001), 639–672 | DOI | MR | Zbl

[14] Wschebor M., “On crossings of Gaussian fields”, Stochastic Process. Appl., 14:2 (1983), 147–155 | DOI | MR | Zbl