Stability of the overdamped Langevin equation in double-well potential

TL;DR

This paper analyzes the stability properties of the overdamped Langevin equation in a double-well potential, identifying stable and unstable equilibria and establishing conditions for stability in general diffusion processes.

Contribution

It introduces generalized stability conditions for diffusion processes, extending classical results and providing detailed analysis of the Langevin equation in double-well potentials.

Findings

Identification of stable and unstable equilibria

Conditions for stability of diffusion processes

Rate of convergence to stable equilibria

Abstract

In this article, we discuss stability of the one-dimensional overdamped Lange\-vin equation in double-well potential. We determine unstable and stable equilibria, and discuss the rate of convergence to stable ones. Also, we derive conditions for stability of general diffusion processes which generalize the classical and well-known results of Khasminskii 2012.