Dependence of the approximation complexity of random fields on dimension
Teoriâ veroâtnostej i ee primeneniâ, Tome 54 (2009) no. 2, pp. 256-270 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

@article{TVP_2009_54_2_a3,
     author = {N. A. Serdyukova},
     title = {Dependence of the approximation complexity of random fields on dimension},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {256--270},
     year = {2009},
     volume = {54},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2009_54_2_a3/}
}
TY  - JOUR
AU  - N. A. Serdyukova
TI  - Dependence of the approximation complexity of random fields on dimension
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 2009
SP  - 256
EP  - 270
VL  - 54
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TVP_2009_54_2_a3/
LA  - ru
ID  - TVP_2009_54_2_a3
ER  - 
%0 Journal Article
%A N. A. Serdyukova
%T Dependence of the approximation complexity of random fields on dimension
%J Teoriâ veroâtnostej i ee primeneniâ
%D 2009
%P 256-270
%V 54
%N 2
%U http://geodesic.mathdoc.fr/item/TVP_2009_54_2_a3/
%G ru
%F TVP_2009_54_2_a3
N. A. Serdyukova. Dependence of the approximation complexity of random fields on dimension. Teoriâ veroâtnostej i ee primeneniâ, Tome 54 (2009) no. 2, pp. 256-270. http://geodesic.mathdoc.fr/item/TVP_2009_54_2_a3/

[1] Adler R. J., An Introduction to Continuity, Extrema, and Related Topics for General Gaussian Processes, IMS Lecture Notes Monogr. Ser., 12, IMS, Hayward, 1990, 160 pp. | MR | Zbl

[2] Anderson T. W., Darling D. A., “Asymptotic theory of certain “goodness of fit” criteria based on stochastic processes”, Ann. Math. Statist., 23 (1952), 193–212 | DOI | MR | Zbl

[3] Beghin L., Nikitin Ya., Orsingher E., “Exact small ball constants for some Gaussian processes under $L^2$-norm”, Zap. nauchn. sem. POMI, 298, 2003, 5–21 | MR | Zbl

[4] Bellman R., Adaptive Control Processes: a Guided Tour, Princeton Univ. Press, Princeton, 1961, 255 pp. | MR | Zbl

[5] Blum J. R., Kiefer J., Rosenblatt M., “Distribution free tests of independence based on the sample distribution function”, Ann. Math. Statist., 32:2 (1961), 485–498 | DOI | MR | Zbl

[6] Buslaev A. P., Seleznjev O. V., “On certain extremal problems in the theory of approximation of random processes”, East J. Approx., 5:4 (1999), 467–481 | MR | Zbl

[7] Csörgő M., Horváth L., Limit Theorems in Change-point Analysis, Wiley, Chichester, 1997, 414 pp.

[8] Deheuvels P., “An asymptotic decomposition for multivariate distribution-free tests of independence”, J. Multivariate Anal., 11 (1981), 102–113 | DOI | MR | Zbl

[9] Dugue D., “Sur des tests d'indépendence “indépendants de la loi””, C. R. Acad. Sci., 281 (1975), 1103–1104 | MR | Zbl

[10] Gnedenko B. V., Kolmogorov A. N., Predelnye raspredeleniya dlya summ nezavisimykh sluchainykh velichin, GTTI, M.–L., 1949, 264 pp. | MR

[11] Henze N., Nikitin Ya. Yu., “A new approach to goodness-of-fit testing based on the integrated empirical process”, J. Nonparametr. Statist., 12 (2000), 391–416 | DOI | MR | Zbl

[12] Hoeffding W., “A non-parametric test of independence”, Ann. Math. Statist., 19 (1948), 546–557 | DOI | MR | Zbl

[13] Koning A. J., Protasov V., “Tail behaviour of Gaussian processes with applications to the Brownian pillow”, J. Multivariate Anal., 87:2 (2003), 370–397 | DOI | MR | Zbl

[14] Kühn T., Linde W., “Optimal series representation of fractional Brownian sheets”, Bernoulli, 8:5 (2002), 669–696 | MR | Zbl

[15] Lifshits M. A., Tulyakova E. V., “Curse of dimensionality in approximation of random fields”, Probab. Math. Statist., 26:1 (2006), 97–112 | MR | Zbl

[16] Petrov V. V., Summy nezavisimykh sluchainykh velichin, Nauka, M., 1972, 416 pp. | MR

[17] Petrov V. V., Predelnye teoremy dlya summ nezavisimykh sluchainykh velichin, Nauka, M., 1987, 320 pp. | MR

[18] Pycke J.-R., “Multivariate extensions of the Anderson–Darling process”, Statist. Probab. Lett., 63:4 (2003), 387–399 | DOI | MR | Zbl

[19] Karhunen K., “Zur Spektraltheorie stochastischer Prozesse”, Ann. Acad. Sci. Fennicae, 34 (1946), 1–7 | MR

[20] Karhunen K., “Über lineare Methoden in der Wahrscheinlichkeitsrechnung”, Ann. Acad. Sci. Fennicae, 37 (1947), 3–79 | MR

[21] Kosambi D. D., “Statistics in function space”, J. Indian Math. Soc. (N.S.), 7 (1943), 76–88 | MR | Zbl

[22] Lifshits M. A., Gaussovskie sluchainye funktsii, TViMS, Kiev, 1995, 246 pp. | Zbl

[23] Loève M., “Fonctions aléatoires de second ordre”, Revue Sci., 84 (1946), 195–206 | MR

[24] Obukhov A. M., “Statisticheskoe opisanie nepreryvnykh polei”, Trudy Geofiz. in-ta AN SSSR, 24(151) (1954), 3–42 | Zbl

[25] Pugachev V. S., “Obschaya teoriya korrelyatsii sluchainykh funktsii”, Izv. AN SSSR, ser. matem., 17:5 (1953), 401–420

[26] Ritter K., Average-case analysis of numerical problems, Lecture Notes in Math., 1733, 2000, 1–254 | MR | Zbl

[27] Sabelfeld K., “Expansion of random boundary excitations for elliptic PDEs”, Monte Carlo Methods Appl., 13:5–6 (2007), 405–453 | MR | Zbl

[28] van der Vaart A. W., Wellner J. A., Weak Convergence and Empirical Processes with Applications to Statistics, Springer Series in Statistics, Springer-Verlag, New York, 1996, 508 pp. | MR

[29] Watson G. S., “Goodness-of-fit tests on a circle”, Biometrika, 48 (1961), 109–114 | MR | Zbl

[30] Woźniakowski H., “Average case complexity of linear multivariate problems. Part I: Theory. Part II: Applications”, J. Complexity, 8:4 (1992), 337–372 ; 373–392 | DOI | MR | Zbl | MR | Zbl

[31] Woźniakowski H., “Tractability and strong tractability of linear multivariate problems”, J. Complexity, 10:1 (1994), 96–128 | DOI | MR | Zbl

[32] Woźniakowski H., “Tractability and strong tractability of multivariate tensor product problems”, J. Computing and Information, 4 (1994), 1–19 | MR

[33] Woźniakowski H., “Tractability of multivariate problems for weighted spaces of functions”, Approximation and Probability, Banach Center Publ., 72, Polish Acad. Sci., Warsaw, 2006, 407–427 | MR | Zbl