Rigorous results for mean first-passage time of harmonically trapped particle

Przemyslaw Chelminiak

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arXiv · 2412.03165

Rigorous results for mean first-passage time of harmonically trapped particle

Przemyslaw Chelminiak

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Abstract

The Ornstein-Uhlenbeck process of diffusion in the harmonic potential is re-examined in the context of the first-passage time problem. We investigate this problem to the extent that it has not yet been fully resolved and demonstrate exact novel results. They mainly concern the mean first-passage time for a particle diffusing downward and upward in the harmonic potential. We verify the main results of this paper by using a number of analytical techniques.

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Przemyslaw Chelminiak. 2024-12-04. Rigorous results for mean first-passage time of harmonically trapped particle. https://arxiv.org/abs/2412.03165

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