Geodesic
Small deviation asymptotics for Matern processes and fields under weighted quadratic norm
Teoriâ veroâtnostej i ee primeneniâ, Tome 55 (2010) no. 1, pp. 187-195 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

@article{TVP_2010_55_1_a13,
     author = {R. S. Pusev},
     title = {Small deviation asymptotics for {Matern} processes and fields under weighted quadratic norm},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {187--195},
     year = {2010},
     volume = {55},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2010_55_1_a13/}
}
TY  - JOUR
AU  - R. S. Pusev
TI  - Small deviation asymptotics for Matern processes and fields under weighted quadratic norm
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 2010
SP  - 187
EP  - 195
VL  - 55
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TVP_2010_55_1_a13/
LA  - ru
ID  - TVP_2010_55_1_a13
ER  - 
%0 Journal Article
%A R. S. Pusev
%T Small deviation asymptotics for Matern processes and fields under weighted quadratic norm
%J Teoriâ veroâtnostej i ee primeneniâ
%D 2010
%P 187-195
%V 55
%N 1
%U http://geodesic.mathdoc.fr/item/TVP_2010_55_1_a13/
%G ru
%F TVP_2010_55_1_a13
R. S. Pusev. Small deviation asymptotics for Matern processes and fields under weighted quadratic norm. Teoriâ veroâtnostej i ee primeneniâ, Tome 55 (2010) no. 1, pp. 187-195. http://geodesic.mathdoc.fr/item/TVP_2010_55_1_a13/

[1] Li W. V., Shao Q. M., “Gaussian processes: inequalities, small ball probabilities and applications”, Stochastic Processes: Theory and Methods, Handbook Statist., 19, North-Holland, Amsterdam, 2001, 533–597 | MR | Zbl

[2] Lifshits M. A., “Asymptotic behavior of small ball probabilities”, Proceedings of the Seventh International Vilnius conference on Probability Theory and Mathematical Statistics, VSP/TEV, Utrecht/Vilnius, 1999, 453–468

[3] Nazarov A. I., Nikitin Ya. Yu., “Exact $L_2$-small ball behavior of integrated Gaussian processes and spectral asymptotics of boundary value problems”, Probab. Theory Related Fields, 129:4 (2004), 469–494 | DOI | MR | Zbl

[4] Nazarov A. I., “O tochnoi konstante v asimptotike malykh uklonenii v $L_2$-norme nekotorykh gaussovskikh protsessov”, Nelineinye uravneniya i matematicheskii analiz, Problemy matem. analiza, 26, T. Rozhkovskaya, Novosibirsk, 2003, 179–214

[5] Nazarov A. I., Pusev R. S., “Tochnaya asimptotika malykh uklonenii v $L_2$-norme s vesom dlya nekotorykh gaussovskikh protsessov”, Zap. nauch. sem. POMI, 364, 2009, 166–199

[6] Matérn B., Spatial Variation, Springer-Verlag, Berlin, 1986, 151 pp. | MR | Zbl

[7] Yaglom A. M., Korrelyatsionnaya teoriya statsionarnykh sluchainykh funktsii s primerami iz meteorologii, Gidrometeoizdat, L., 1981, 280 pp.

[8] Stein M., “Design and Analysis of Computer Experiments”, Comment. Statist. Sci., 4 (1989), 432–433 | DOI | MR

[9] Williams B. J., Santner T. J., Notz W. I., “Sequential design of computer experiments to minimize integrated response functions”, Statist. Sinica, 10 (2000), 1133–1152 | MR | Zbl

[10] Loh W.-L., “Fixed-domain asymptotics for a subclass of Matérn-type Gaussian random fields”, Ann. Statist., 33:5 (2005), 2344–2394 | DOI | MR | Zbl

[11] Li W. V., “Comparison results for the lower tail of Gaussian seminorms”, J. Theoret. Probab., 5:1 (1992), 1–31 | DOI | MR

[12] Pusev R. S., “Malye ukloneniya polei i protsessov Materna v gilbertovoi norme”, Dokl. RAN, 422:6 (2008), 741–743 | MR | Zbl

[13] Rasmussen C. E., Williams C. K. I., Gaussian Processes for Machine Learning, MIT Press, Cambridge, 2006, 248 pp. | MR | Zbl

[14] Widom H., “Asymptotic behavior of the eigenvalues of certain integral equations”, Trans. Amer. Math. Soc., 109 (1963), 278–295 | DOI | MR | Zbl

[15] Karol' A., Nazarov A., Nikitin Y., “Small ball probabilities for Gaussian random fields and tensor products of compact operators”, Trans. Amer. Math. Soc., 360:3 (2008), 1443–1474 | DOI | MR | Zbl

[16] Naimark M. A., Lineinye differentsialnye operatory, Nauka, M., 1969, 526 pp. | MR

[17] Titchmarsh E., Teoriya funktsii, Nauka, M., 1980, 463 pp. | MR | Zbl