  Solar dynamics and turbulence occur at all heights of the solar atmosphere
and could be described as stochastic processes. We propose that finite lifetime
transients recurring at a certain place could trigger quasi-periodic processes
in the associated structures. In this study, we developed a mathematical model
for finite lifetime and randomly occurring transients, and found that
quasi-periodic processes, with period longer than the time scale of the
transients, are detectable intrinsically in form of trains. We simulate their
propagation in an empirical solar atmospheric model with chromosphere,
transition region and corona. We found that, due to the filtering effect of the
chromospheric cavity, only the resonance period of the acoustic resonator is
able to propagate to the upper atmosphere, such a scenario is applicable to
slow magnetoacoustic waves in sunspots and active regions. If the thermal
structure of the atmosphere is less wild and acoustic resonance does not take
effect, the long period oscillations could propagate to the upper atmosphere.
Such case would be more likely to occur at polar plumes.
