application to dynamic bifurcations and threshold crossings
Journal of Statistical Physics
100 1097 (2000)
Department of Mathematics, University College London.
Gower Street WC1E 6BT, England.
Departamento de Matemáticas
Universidad Carlos III de Madrid
Avenida de la Universidad 30
28911 Leganés, Madrid, Spain
For the dynamic pitchfork bifurcation in the presence of white noise,
the statistics of the last time at zero are calculated as a function
of the noise level and the rate of change of the parameter. 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.