This study considers Kramers' diffusion problem, which seeks to calculate the rate of escape of a particle from one potential well over a barrier, to another presumably deeper and therefore more stable well. A new approach, based on the solution of a singularly perturbed boundary value problem is proposed. The rate of escape is related to the first passage time from the domain of attraction of the stable point corresponding to the first well. The first passage time is then characterized via the Ito calculus, as a solution of an elliptic partial differential equation of singular perturbation type. Finally this equation is solved asymptotically.
ASJC Scopus subject areas
- Applied Mathematics