英文标题：
《Explicit Asymptotics on First Passage Times of Diffusion Processes》
---
作者：
Angelos Dassios and Luting Li
---
最新提交年份：
2018
---
英文摘要：
We introduce a unified framework for solving first passage times of time-homogeneous diffusion processes. According to the killed version potential theory and the perturbation theory, we are able to deduce closed-form solutions for probability densities of single-sided level crossing problem. The framework is applicable to diffusion processes with continuous drift functions, and a recursive system in the frequency domain has been provided. Besides, we derive a probabilistic representation for error estimation. The representation can be used to evaluate deviations in perturbed density functions. In the present paper, we apply the framework to Ornstein-Uhlenbeck and Bessel processes to find closed-form approximations for their first passage times; another successful application is given by the exponential-Shiryaev process. Numerical results are provided at the end of this paper.
---
中文摘要：
我们引入了一个统一的框架来求解时间齐次扩散过程的首次通过时间。根据killed势理论和摄动理论，我们可以推导出单侧平交道口问题概率密度的闭式解。该框架适用于具有连续漂移函数的扩散过程，并提供了频域递归系统。此外，我们推导了误差估计的概率表示。该表示法可用于计算扰动密度函数中的偏差。在本文中，我们将该框架应用于Ornstein-Uhlenbeck和Bessel过程，以找到其第一次通过时间的闭合形式近似；指数Shiryaev过程给出了另一个成功的应用。最后给出了数值结果。
---
分类信息：

一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
--
一级分类：Mathematics 数学
二级分类：Numerical Analysis 数值分析
分类描述：Numerical algorithms for problems in analysis and algebra, scientific computation
分析和代数问题的数值算法，科学计算
--
一级分类：Quantitative Finance 数量金融学
二级分类：Mathematical Finance 数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
--

---
PDF下载：
-->