  We analyze the generation rates and preparation fidelities of photon triplet
states in pulsed cascaded parametric down-conversion (PDC) under realistic
experimental circumstances. As a model system, we assume a monolithically
integrated device with negligible interface loss between the two consecutive
PDC stages. We model the secondary down-conversion process in terms of a lossy
channel and provide a detailed analysis of noise contributions. Taking variable
pump powers into account, we estimate the impact of higher-order photon
contributions and conversion processes on the achievable coincidence
probabilities. At mean photon numbers of $\langle m\rangle\sim0.25$ photons per
pulse behind the first PDC stage, we expect around $4.0$ genuine photon
triplets per hour. Additionally, we discuss fundamental limitations of our
model system as well as feasible improvements to the detectable photon triplet
rate.
