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

TL;DR

This paper provides exact analytical results for the mean first-passage time of a particle in a harmonic potential, addressing unresolved aspects of the Ornstein-Uhlenbeck process with rigorous verification.

Contribution

It introduces novel exact solutions for the mean first-passage time in the Ornstein-Uhlenbeck process, expanding understanding of diffusion in harmonic potentials.

Findings

Exact formulas for mean first-passage time downward and upward in harmonic potential

Verification of results through multiple analytical techniques

Addresses previously unresolved aspects of the Ornstein-Uhlenbeck process

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.