The exit problem for certain dynamical systems with small poisson disturbances

Abstract

The mean first passage time from the inside to the outside of a finite interval for the solution of a differential equation perturbed by Poisson noise may have a discontinuity at one end of the interval. When the size ofthe perturbation is small, the magnitude of the discontinuity can be large and difficult to calculate. In this paper asymptotic approximations for the size of the discontinuity are derived in two cases of practical interest. The approximations show that the discontinuity grows exponentially.