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Explicit asymptotic on first passage times of diffusion processes

Dassios, Angelos and Li, Luting (2020) Explicit asymptotic on first passage times of diffusion processes. Advances in Applied Probability, 52 (2). ISSN 0001-8678

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We introduce a unified framework for solving first passage times of time- homogeneous diffusion processes. According to the potential theory and the perturbation theory, we are able to deduce closed-form truncated probability densities, as asymptotics or approximations to the original first passage time densities, for the single-side level crossing problems. The framework is applicable to diffusion processes with continuous drift functions; especially, for bounded drift functions, we show that the perturbation series converges. In the present paper, we demonstrate examples of applying our framework to the Ornstein-Uhlenbeck, Bessel, exponential-Shiryaev (studied in [13]), and the hypergeometric diffusion [8] processes. The purpose of this paper is to provide a fast and accurate approach to estimate first passage time densities of various diffusion processes.

Item Type: Article
Official URL:
Additional Information: © 2020 Applied Probability Trust
Divisions: Statistics
Subjects: Q Science > QA Mathematics
H Social Sciences > HA Statistics
Date Deposited: 17 Jan 2020 09:03
Last Modified: 25 Aug 2022 23:16

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