Standard

Chung's Law and the Csáki Function. / Gorn, Natalia; Lifshits, Mikhail.

In: Journal of Theoretical Probability, Vol. 12, No. 2, 01.01.1999, p. 399-420.

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

Harvard

Gorn, N & Lifshits, M 1999, 'Chung's Law and the Csáki Function', Journal of Theoretical Probability, vol. 12, no. 2, pp. 399-420. https://doi.org/10.1023/A:1021678111442

APA

Gorn, N., & Lifshits, M. (1999). Chung's Law and the Csáki Function. Journal of Theoretical Probability, 12(2), 399-420. https://doi.org/10.1023/A:1021678111442

Vancouver

Gorn N, Lifshits M. Chung's Law and the Csáki Function. Journal of Theoretical Probability. 1999 Jan 1;12(2):399-420. https://doi.org/10.1023/A:1021678111442

Author

Gorn, Natalia ; Lifshits, Mikhail. / Chung's Law and the Csáki Function. In: Journal of Theoretical Probability. 1999 ; Vol. 12, No. 2. pp. 399-420.

BibTeX

@article{ccb48466ae3345fcb33f182f29d1f11a,
title = "Chung's Law and the Cs{\'a}ki Function",
abstract = "We have found the limit ℒh = lim inf (log2 T)2/3 T → ∞ ∥W(T·)/(2T log2 T)1/2 - h∥ for a Wiener process W and a class of twice weakly differentiable functions h ∈ C[0, 1], thus solving the problem of the convergence rate in Chung's functional law for the so-called {"}slowest points{"}. Our description is closely related to an interesting functional emerging from a large deviation problem for the Wiener process in a strip.",
keywords = "Large deviation, Wiener process",
author = "Natalia Gorn and Mikhail Lifshits",
year = "1999",
month = jan,
day = "1",
doi = "10.1023/A:1021678111442",
language = "English",
volume = "12",
pages = "399--420",
journal = "Journal of Theoretical Probability",
issn = "0894-9840",
publisher = "Springer Nature",
number = "2",

}

RIS

TY - JOUR

T1 - Chung's Law and the Csáki Function

AU - Gorn, Natalia

AU - Lifshits, Mikhail

PY - 1999/1/1

Y1 - 1999/1/1

N2 - We have found the limit ℒh = lim inf (log2 T)2/3 T → ∞ ∥W(T·)/(2T log2 T)1/2 - h∥ for a Wiener process W and a class of twice weakly differentiable functions h ∈ C[0, 1], thus solving the problem of the convergence rate in Chung's functional law for the so-called "slowest points". Our description is closely related to an interesting functional emerging from a large deviation problem for the Wiener process in a strip.

AB - We have found the limit ℒh = lim inf (log2 T)2/3 T → ∞ ∥W(T·)/(2T log2 T)1/2 - h∥ for a Wiener process W and a class of twice weakly differentiable functions h ∈ C[0, 1], thus solving the problem of the convergence rate in Chung's functional law for the so-called "slowest points". Our description is closely related to an interesting functional emerging from a large deviation problem for the Wiener process in a strip.

KW - Large deviation

KW - Wiener process

UR - http://www.scopus.com/inward/record.url?scp=0033441792&partnerID=8YFLogxK

U2 - 10.1023/A:1021678111442

DO - 10.1023/A:1021678111442

M3 - Article

AN - SCOPUS:0033441792

VL - 12

SP - 399

EP - 420

JO - Journal of Theoretical Probability

JF - Journal of Theoretical Probability

SN - 0894-9840

IS - 2

ER -

ID: 37011253