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arXiv · 2603.02054

Exact Asymptotics for the Exit Time Probabilities of Scalar Ornstein-Uhlenbeck Bridges

Feng Zhao·Yang Li·Jianlong Wang·Xianbin Liu·Dongping Jin
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Abstract

This paper aims to derive accurate asymptotic estimates for the exit time probabilities of scalar Ornstein-Uhlenbeck (OU) bridges. The exit time probabilities are expressed as an asymptotic series in powers of a small parameter that characterizes the intensity of the noise inputs. It is shown that the series is valid in certain regions where all its terms are smooth functions. The results enable an accurate evaluation of the probability for a corresponding OU process to escape from a domain before a specified time, provided its initial and terminal states are known.

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Feng Zhao, Yang Li, Jianlong Wang, Xianbin Liu, Dongping Jin. 2026-03-02. Exact Asymptotics for the Exit Time Probabilities of Scalar Ornstein-Uhlenbeck Bridges. https://arxiv.org/abs/2603.02054

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