A revised analysis of the exit problem at weak noise, and a simpler computation of the quasipotential with two variables

TL;DR

This paper introduces a new method for analyzing exit problems under weak noise, simplifying quasipotential computation for two-variable systems and resolving contradictions in previous approaches.

Contribution

It presents a revised approach that removes contradictions in weak noise exit analysis and simplifies quasipotential calculation without Hamiltonian systems for two variables.

Findings

New approach applicable to mean exit time and location

Simplified quasipotential computation for two-variable systems

Addresses previous methodological contradictions

Abstract

A new approach for the weak noise analysis of exit problems removes an intrinsic contradiction of an existing method. It applies for both the mean time and the location of the exits; novel outcomes mainly concern the exits from entire domains of attraction. Moreover, the involved quasipotential is obtained without use of a Hamiltonian system in the case of two variables.