  We investigate the role of noise in the phenomenon of stochastic
synchronization of switching events in a rocked, overdamped bistable potential
driven by white Gaussian noise, the archetype description of Stochastic
Resonance. We present a new approach to the stochastic counting process of
noise-induced switching events: starting from the Markovian dynamics of the
nonstationary, continuous particle dynamics one finds upon contraction onto two
states a non-Markovian renewal dynamics. The output frequency is determined as
the velocity of the underlying discrete phase dynamics. The phenomenon of
noise-assisted phase synchronization is investigated in terms of an effective,
instantaneous phase diffusion. The theory is applied to rectangular-shaped
rocking signals versus increasing input-noise strengths. Precise numerical
simulations corroborate very favorably our analytical results. The novel
theoretical findings are also compared with prior findings.
