On the behavior of diffusion processes with traps

TL;DR

This paper studies how diffusion processes with strong inward drifts in certain regions behave as the drift becomes infinitely large, leading to trapping and metastability over exponential time scales.

Contribution

It characterizes the limiting behavior and metastable distributions of diffusion processes with large inward drifts in trapping domains.

Findings

Processes become trapped in domains with large inward drift

Exit times from trapping regions grow exponentially

Metastable distributions describe long-term behavior

Abstract

We consider processes that coincide with a given diffusion process outside a finite collection of domains. In each of the domains, there is, additionally, a large drift directed towards the interior of the domain. We describe the limiting behavior of the processes as the magnitude of the drift tends to infinity, and thus the domains become trapping, with the time to exit the domains being exponentially large. In particular, in exponential time scales, metastable distributions between the trapping regions are considered.