Explicit asymptotic on first passage times of diffusion processes

Dassios, Angelos ORCID: 0000-0002-3968-2366 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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Abstract

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:	https://www.cambridge.org/core/journals/journal-of...
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:	12 Dec 2024 02:02
URI:	http://eprints.lse.ac.uk/id/eprint/103087

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