  We consider the drift and diffusion properties of periodically driven renewal
processes. These processes are defined by a periodically time dependent waiting
time distribution, which governs the interval between subsequent events. We
show that the growth of the cumulants of the number of events is asymptotically
periodic and develop a theory which relates these periodic growth coefficients
to the waiting time distribution defining the periodic renewal process. The
first two coefficients, which are the mean frequency and effective diffusion
coefficient of the number of events are considered in greater detail. They may
be used to quantify stochastic synchronization.
