具有破碎漂移的Ornstein-Uhlenbeck过程的首次通过时间密度

IF 0.5 4区数学 Q4 STATISTICS & PROBABILITY

Stochastic Models Pub Date : 2022-02-07 DOI:10.1080/15326349.2022.2026790

S. Ankirchner, Christophette Blanchet-Scalliet, Diana Dorobantu, Laura Gay

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引用次数: 1

摘要

我们考虑了一个小于零和大于零的不同漂移率的Ornstein-Uhlenbeck过程。我们第一次导出密度的解析表达式，当过程达到给定水平时。通过时间密度与过程的联合规律及其运行极限相联系，并给出了联合密度/分布函数的解析公式。数值实验结果表明，与基于模拟的方法相比，我们的公式可以更快地对联合律和首次通过时间密度进行数值计算。

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First passage time density of an Ornstein–Uhlenbeck process with broken drift

Abstract We consider an Ornstein–Uhlenbeck process with different drift rates below and above zero. We derive an analytic expression for the density of the first time, where the process hits a given level. The passage time density is linked to the joint law of the process and its running supremum, and we also provide an analytic formula of the joint density/distribution function. Results from a numerical experiment reveal that our formulas allow to numerically evaluate the joint law and the density of the first passage time faster than a simulation-based method.

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来源期刊

Stochastic Models 数学-统计学与概率论

CiteScore

1.30

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Stochastic Models publishes papers discussing the theory and applications of probability as they arise in the modeling of phenomena in the natural sciences, social sciences and technology. It presents novel contributions to mathematical theory, using structural, analytical, algorithmic or experimental approaches. In an interdisciplinary context, it discusses practical applications of stochastic models to diverse areas such as biology, computer science, telecommunications modeling, inventories and dams, reliability, storage, queueing theory, mathematical finance and operations research.