  We present a simple stochastic mechanism which generates pulse trains
exhibiting a power law distribution of the pulse intervals and a $1/f^\alpha$
power spectrum over several decades at low frequencies with $\alpha$ close to
one. The essential ingredient of our model is a fluctuating threshold which
performs a Brownian motion. Whenever an increasing potential $V(t)$ hits the
threshold, $V(t)$ is reset to the origin and a pulse is emitted. We show that
if $V(t)$ increases linearly in time, the pulse intervals can be approximated
by a random walk with multiplicative noise. Our model agrees with recent
experiments in neurobiology and explains the high interpulse interval
variability and the occurrence of $1/f^\alpha$ noise observed in cortical
neurons and earthquake data.
