On the distribution of quadratic functionals of the ordinary and fractional Brownian motions

被引：2

作者：

Tanaka, Katsuto ^{[1
]}

机构：

[1] Hitotsubashi Univ, Grad Sch Econ, Tokyo 1868601, Japan

来源：

JOURNAL OF STATISTICAL PLANNING AND INFERENCE | 2008年 / 138卷 / 11期

关键词：

fractional Brownian motion; long-memory; Fredholm determinant;

D O I：

10.1016/j.jspi.2005.12.015

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 discuss some distributional properties of quadratic functionals of the ordinary and fractional Brownian motions (fBms). As far as the ordinary Brownian motion (Bm) is concerned, those properties have been established extensively. A transition from the Bm to the fBm is not straightforward. Some difficulties associated with dealing with the fBm are explained, and a way to solving the problem is indicated, and some conjectures are given. (C) 2008 Elsevier B.V. All rights reserved.

引用

页码：3525 / 3537

页数：13

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