Small ball constants and tight eigenvalue asymptotics for fractional Brownian motions

被引：25

作者：

Bronski, JC ^{[1
]}

机构：

[1] Univ Illinois, Dept Math, Urbana, IL 61820 USA

来源：

JOURNAL OF THEORETICAL PROBABILITY | 2003年 / 16卷 / 01期

基金：

美国国家科学基金会;

关键词：

fractional Brownian motion; small ball probabilities; eigenvalue asymptotics; Karhunen-Loeve expansion;

D O I：

10.1023/A:1022226420564

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In this paper we prove rigorous large n asymptotics for the Karhunen- Loeve eigenvalues of a fractional Brownian motion. From the asymptotics of the eigenvalues the exact constants for small L-2 ball estimates for fractional Brownian motions follows in a straightforward way.

引用

页码：87 / 100

页数：14

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