Standard

Entropie métrique de l'opérateur d'intégration et probabilités de petites boules relatives au drap brownien. / Dunker, Thomas; Kühn, Thomas; Lifshits, Mikhail; Linde, Werner.

In: Comptes Rendus de l'Academie des Sciences - Series I: Mathematics, Vol. 326, No. 3, 01.01.1998, p. 347-352.

Research output: Contribution to journal › Article › peer-review

Harvard

Dunker, T, Kühn, T, Lifshits, M & Linde, W 1998, 'Entropie métrique de l'opérateur d'intégration et probabilités de petites boules relatives au drap brownien', Comptes Rendus de l'Academie des Sciences - Series I: Mathematics, vol. 326, no. 3, pp. 347-352. https://doi.org/10.1016/S0764-4442(97)82993-X

APA

Dunker, T., Kühn, T., Lifshits, M., & Linde, W. (1998). Entropie métrique de l'opérateur d'intégration et probabilités de petites boules relatives au drap brownien. Comptes Rendus de l'Academie des Sciences - Series I: Mathematics, 326(3), 347-352. https://doi.org/10.1016/S0764-4442(97)82993-X

Vancouver

Dunker T, Kühn T, Lifshits M, Linde W. Entropie métrique de l'opérateur d'intégration et probabilités de petites boules relatives au drap brownien. Comptes Rendus de l'Academie des Sciences - Series I: Mathematics. 1998 Jan 1;326(3):347-352. https://doi.org/10.1016/S0764-4442(97)82993-X

Author

Dunker, Thomas ; Kühn, Thomas ; Lifshits, Mikhail ; Linde, Werner. / Entropie métrique de l'opérateur d'intégration et probabilités de petites boules relatives au drap brownien. In: Comptes Rendus de l'Academie des Sciences - Series I: Mathematics. 1998 ; Vol. 326, No. 3. pp. 347-352.

BibTeX

@article{6ae888d97e844fa08df5cc1caa90fe16,
title = "Entropie m{\'e}trique de l'op{\'e}rateur d'int{\'e}gration et probabilit{\'e}s de petites boules relatives au drap brownien",
abstract = "Let Td : L2([0, 1]d) → C([0. 1]d) be the d-dimensional integration operator. We show that its Kolmogorov and entropy numbers decrease with order at least k-1 (log k)d.-1/2. From this we derive that the small ball probabilities of the Brownian sheet on [0, 1]d under the C([0, 1]d)-norm can be estimated from below by exp(-Cε-2|log ε|2d-1), which improves the best known lower bounds considerably. We also get similar results with respect to certain Orlicz norms.",
author = "Thomas Dunker and Thomas K{\"u}hn and Mikhail Lifshits and Werner Linde",
year = "1998",
month = jan,
day = "1",
doi = "10.1016/S0764-4442(97)82993-X",
language = "English",
volume = "326",
pages = "347--352",
journal = "Comptes Rendus Mathematique",
issn = "1631-073X",
publisher = "Elsevier",
number = "3",

}

RIS

TY - JOUR

T1 - Entropie métrique de l'opérateur d'intégration et probabilités de petites boules relatives au drap brownien

AU - Dunker, Thomas

AU - Kühn, Thomas

AU - Lifshits, Mikhail

AU - Linde, Werner

PY - 1998/1/1

Y1 - 1998/1/1

N2 - Let Td : L2([0, 1]d) → C([0. 1]d) be the d-dimensional integration operator. We show that its Kolmogorov and entropy numbers decrease with order at least k-1 (log k)d.-1/2. From this we derive that the small ball probabilities of the Brownian sheet on [0, 1]d under the C([0, 1]d)-norm can be estimated from below by exp(-Cε-2|log ε|2d-1), which improves the best known lower bounds considerably. We also get similar results with respect to certain Orlicz norms.

AB - Let Td : L2([0, 1]d) → C([0. 1]d) be the d-dimensional integration operator. We show that its Kolmogorov and entropy numbers decrease with order at least k-1 (log k)d.-1/2. From this we derive that the small ball probabilities of the Brownian sheet on [0, 1]d under the C([0, 1]d)-norm can be estimated from below by exp(-Cε-2|log ε|2d-1), which improves the best known lower bounds considerably. We also get similar results with respect to certain Orlicz norms.

UR - http://www.scopus.com/inward/record.url?scp=0031996159&partnerID=8YFLogxK

U2 - 10.1016/S0764-4442(97)82993-X

DO - 10.1016/S0764-4442(97)82993-X

M3 - Article

AN - SCOPUS:0031996159

VL - 326

SP - 347

EP - 352

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

SN - 1631-073X

IS - 3

ER -

ID: 43811346