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• W2809269638 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." @default.
• W2809269638 created "2018-06-29" @default.
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• W2809269638 date "2020-06-01" @default.
• W2809269638 modified "2023-10-17" @default.
• W2809269638 title "Explicit asymptotics on first passage times of diffusion processes" @default.
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• W2809269638 doi "https://doi.org/10.1017/apr.2020.13" @default.
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