SMOLUCHOWSKI–KRAMERS APPROXIMATION AND EXIT PROBLEMS

Abstract

As is known, the solution of problem (1) converges to the solution of problem (3) uniformly on any finite time interval as μ ↓ 0. We study relations between large deviations for these two processes [Formula: see text] and [Formula: see text] as ε ↓ 0. A special attention is paid to the case of linear systems, when the quasi-potential is calculated explicitly.