Representations of the first hitting time density of an Ornstein-Uhlenbeck process

被引：149

作者：

Alili, A ^{[1
]}

Patie, P

Pedersen, JL

机构：

[1] Univ Warwick, Dept Stat, Coventry CV4 7AL, W Midlands, England

[2] RiskLab, Dept Math, Zurich, Switzerland

[3] Univ Copenhagen, Dept Appl Math & Stat, Copenhagen, Denmark

来源：

STOCHASTIC MODELS | 2005年 / 21卷 / 04期

关键词：

Bessel bridge; Fourier transform; hitting time density; Laplace transform; Ornstein-Uhlenbeck process;

D O I：

10.1080/15326340500294702

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：

Three expressions are provided for the first hitting tine density of an Ornstein-Uhlenbeck process to reach a fixed level. The first hinges on an eigenvalue expansion involving zeros of the parabolic cylinder functions. The second is an, integral representation involving some special functions whereas the third is given in terms of a functional of a 3-dimensional Bessel badge. The expressions are used for approximating the density.

引用

页码：967 / 980

页数：14

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