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arXiv · 1411.3598

First Exit Times of Harmonically Trapped Particles: A Didactic Review

D. S. Grebenkov
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Abstract

We revise the classical problem of characterizing first exit times of a harmonically trapped particle whose motion is described by one- or multi-dimensional Ornstein-Uhlenbeck process. We start by recalling the main derivation steps of a propagator using Langevin and Fokker-Planck equations. The mean exit time, the moment-generating function, and the survival probability are then expressed through confluent hypergeometric functions and thoroughly analyzed. We also present a rapidly converging series representation of confluent hypergeometric functions that is particularly well suited for numerical computation of eigenvalues and eigenfunctions of the governing Fokker-Planck operator. We discuss several applications of first exit times such as detection of time intervals during which motor proteins exert a constant force onto a tracer in optical tweezers single-particle tracking experiments; adhesion bond dissociation under mechanical stress; characterization of active periods of trend following and mean-reverting strategies in algorithmic trading on stock markets; relation to the distribution of first crossing times of a moving boundary by Brownian motion. Some extensions are described, including diffusion under quadratic double-well potential and anomalous diffusion.

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BibTeXRIS

D. S. Grebenkov. 2014-11-13. First Exit Times of Harmonically Trapped Particles: A Didactic Review. https://doi.org/10.1088/1751-8113/48/1/013001

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