Joint law of an Ornstein-Uhlenbeck process and its supremum

被引：4

作者：

Blanchet-Scalliet, Christophette ^{[1
,3
]}

Dorobantu, Diana ^{[1
,3
]}

Gay, Laura ^{[1
,2
]}

机构：

[1] Univ Lyon, Lyon, France

[2] Inst Camille Jordan, CNRS, UMR 5208, Ecole Cent Lyon, Villeurbanne, France

[3] Univ Lyon 1, ISFA, LSAF, EA 2429, Lyon, France

来源：

JOURNAL OF APPLIED PROBABILITY | 2020年 / 57卷 / 02期

关键词：

Ornstein-Uhlenbeck process; joint law; supremum; endpoint; Fokker-Planck equation; DENSITY;

D O I：

10.1017/jpr.2020.22

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：

LetXbe an Ornstein-Uhlenbeck process driven by a Brownian motion. We propose an expression for the joint density / distribution function of the process and its running supremum. This law is expressed as an expansion involving parabolic cylinder functions. Numerically, we obtain this law faster with our expression than with a Monte Carlo method. Numerical applications illustrate the interest of this result.

引用

页码：541 / 558

页数：18

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