The Annals of Probability

Gaussian Measure of Large Balls in $l_p$

Werner Linde

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Abstract

We study the behaviour of $\mu\{x \in E; \|x\| > t\}$ as $t \rightarrow \infty$ for a Gaussian measure $\mu$ in a Banach or quasi-Banach space in the following cases: 1. $E = l_p, 2 < p < \infty$, and $\mu$ of diagonal form but not necessarily symmetric; 2. $E =$ Hilbert space and $\mu$ arbitrary; 3. $E = l^n_p, 0 < p < 2$, and $\mu$ of diagonal form. While 2 solves a problem of Hweng (1980), 1 and 3 extend some results of Dobric, Marcus and Weber (1988).

Article information

Source
Ann. Probab., Volume 19, Number 3 (1991), 1264-1279.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176990343

Digital Object Identifier
doi:10.1214/aop/1176990343

Mathematical Reviews number (MathSciNet)
MR1112415

Zentralblatt MATH identifier
0736.60004

JSTOR
links.jstor.org

Subjects
Primary: 60B11: Probability theory on linear topological spaces [See also 28C20]
Secondary: 60G15: Gaussian processes 60F10: Large deviations

Keywords
Gaussian measure tail behaviour $l_p$-space

Citation

Linde, Werner. Gaussian Measure of Large Balls in $l_p$. Ann. Probab. 19 (1991), no. 3, 1264--1279. doi:10.1214/aop/1176990343. https://projecteuclid.org/euclid.aop/1176990343


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