STOCHASTIC CALCULUS - APPLICATION TO DYNAMIC BIFURCATIONS AND THRESHOLD CROSSINGS

For the dynamic pitchfork bifurcation in the presence of white noise, the statistics of the last time at zero are calculated as a function o f the noise level epsilon and the rate of change of the parameter mu. The threshold crossing problem used, for example, to model the firing of a single cortical neuron is considered, concentrating on quantities that may be experimentally measurable but have so far received little attention. Expressions For the statistics of pre-threshold excursions , occupation density, and last crossing time of zero are compared with results from numerical generation of paths.