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Small deviation probability via chaining. / Aurzada, Frank; Lifshits, Mikhail.

In: Stochastic Processes and their Applications, Vol. 118, No. 12, 01.12.2008, p. 2344-2368.

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

Harvard

Aurzada, F & Lifshits, M 2008, 'Small deviation probability via chaining', Stochastic Processes and their Applications, vol. 118, no. 12, pp. 2344-2368. https://doi.org/10.1016/j.spa.2008.01.005

APA

Aurzada, F., & Lifshits, M. (2008). Small deviation probability via chaining. Stochastic Processes and their Applications, 118(12), 2344-2368. https://doi.org/10.1016/j.spa.2008.01.005

Vancouver

Aurzada F, Lifshits M. Small deviation probability via chaining. Stochastic Processes and their Applications. 2008 Dec 1;118(12):2344-2368. https://doi.org/10.1016/j.spa.2008.01.005

Author

Aurzada, Frank ; Lifshits, Mikhail. / Small deviation probability via chaining. In: Stochastic Processes and their Applications. 2008 ; Vol. 118, No. 12. pp. 2344-2368.

BibTeX

@article{894c660797334668ac2a19b6c8028661,
title = "Small deviation probability via chaining",
abstract = "We obtain several extensions of Talagrand's lower bound for the small deviation probability using metric entropy. For Gaussian processes, our investigations are focused on processes with sub-polynomial and, respectively, exponential behaviour of covering numbers. The corresponding results are also proved for non-Gaussian symmetric stable processes, both for the cases of critically small and critically large entropy. The results extensively use the classical chaining technique; at the same time they are meant to explore the limits of this method.",
keywords = "Chaining, Gaussian processes, Lower tail probability, Metric entropy, Small deviation, Stable processes",
author = "Frank Aurzada and Mikhail Lifshits",
year = "2008",
month = dec,
day = "1",
doi = "10.1016/j.spa.2008.01.005",
language = "English",
volume = "118",
pages = "2344--2368",
journal = "Stochastic Processes and their Applications",
issn = "0304-4149",
publisher = "Elsevier",
number = "12",

}

RIS

TY - JOUR

T1 - Small deviation probability via chaining

AU - Aurzada, Frank

AU - Lifshits, Mikhail

PY - 2008/12/1

Y1 - 2008/12/1

N2 - We obtain several extensions of Talagrand's lower bound for the small deviation probability using metric entropy. For Gaussian processes, our investigations are focused on processes with sub-polynomial and, respectively, exponential behaviour of covering numbers. The corresponding results are also proved for non-Gaussian symmetric stable processes, both for the cases of critically small and critically large entropy. The results extensively use the classical chaining technique; at the same time they are meant to explore the limits of this method.

AB - We obtain several extensions of Talagrand's lower bound for the small deviation probability using metric entropy. For Gaussian processes, our investigations are focused on processes with sub-polynomial and, respectively, exponential behaviour of covering numbers. The corresponding results are also proved for non-Gaussian symmetric stable processes, both for the cases of critically small and critically large entropy. The results extensively use the classical chaining technique; at the same time they are meant to explore the limits of this method.

KW - Chaining

KW - Gaussian processes

KW - Lower tail probability

KW - Metric entropy

KW - Small deviation

KW - Stable processes

UR - http://www.scopus.com/inward/record.url?scp=55849112671&partnerID=8YFLogxK

U2 - 10.1016/j.spa.2008.01.005

DO - 10.1016/j.spa.2008.01.005

M3 - Article

AN - SCOPUS:55849112671

VL - 118

SP - 2344

EP - 2368

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

SN - 0304-4149

IS - 12

ER -

ID: 37009742