BOUNDS ON MEAN EXIT TIME FOR PURELY TIME-DEPENDENT DRIFT AND DIFFUSION

The mean first exit time is studied for the one-dimensional problem with one-sided exit and purely time-dependent drift and diffusion. Exact mean exit times are derived when the drift coefficient is constant and the diffusion coefficient is bounded. When the drift and diffusion coefficients both vary with time, bounds on mean first exit time are derived. Examples are described that illustrate the usefulness of the results.