Explicit Asymptotics on First Passage Times of Diffusion Processes

Angelos Dassios and Luting Li

Papers from arXiv.org

Abstract: 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.

Date: 2018-06
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Published in Adv. Appl. Probab. 52 (2020) 681-704

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