Diffusion approximation and first passage time problem for a model neuron. II. Outline of a computational method

To account for nonstationary effects the customary diffusion approximations in neuro-biology have to be modified in order to include time-varying terms in the expressions of drift and infinitesimal variance. The evaluation of the statistics of the firing time thus generally requires the use of numerical procedures. In this paper it is shown how one can extend a method due to Durbin (1971) to the case of temporally inhomogeneous diffusion equations by employing a transformation technique. A few simple examples are briefly discussed.