Quasipotentials with more than two variables: new evaluation at equilibrium points of the drift

TL;DR

This paper introduces a new linear matrix equation to evaluate quasipotentials with multiple variables at equilibrium points, improving accuracy and ensuring asymptotic consistency with the Fokker-Planck equation.

Contribution

It presents a novel linear matrix approach for quasipotential evaluation in multi-variable systems, reducing unknowns and enhancing global asymptotic properties.

Findings

New linear matrix equation for quasipotential near equilibrium

Ensures asymptotic fulfillment of the Fokker-Planck equation

Provides an auxiliary result for the exit problem

Abstract

The relevant quasipotential near an equilibrium point is determined by a new linear matrix equation, with less unknowns than an existing (possibly nonlinear) one. This also assures the asymptotic fulfillment of the Fokker-Planck equation, even globally due to the second term in the noise strength. An auxiliary result for the exit problem is derived as well.