Many processes throughout the heliosphere such as flares, CMEs, storms
and substorms have abrupt onsets. The waiting time between these onsets
provides key insights as to the underlying dynamical processes. We
explore the tail of these waiting time distributions in the context of
random processes driven by the solar magnetic activity cycle, which we
approximate by a sinusoidal driver. Analytically, we find that the
distribution of large waiting times of such a process approaches a power
law slope of -2.5 at large enough waiting time, and we find that this
power law is primarily controlled by the conditions when the driving is
minimum. We find that the asymptotic behavior of the waiting time
distributions of solar flares, coronal mass ejections, geomagnetic
storms, and substorms exhibit power laws are in reasonable agreement
with a sinusoidally driven nonstationary Poisson process.