Curve-crossing problem for Gaussian stochastic processes and its application to neural modelling

摘要

A first time crossing problem for Gaussian stochastic process and monotonic time curve is considered and results are discussed with application to neural modelling. Using diffusion approximation of the stochastic process, integral equation for probability density function of the first time crossing has been obtained. Exact solution of the equation is given for two kinds of stochastic processes which have correspondingly infinitesimal and infinitely large correlation time; approximation methods are constructed for processes characterized by intermediate values of this parameter.