  Extended derivations regarding the cumulant-based formulation of higher-order
fluorescence correlation spectroscopy (FCS) are presented. First, we review
multivariate cumulants and their relation to photon counting distributions in
single and multi-detector experiments. Then we derive the factorized
correlation functions which describe system of diffusing and reacting molecules
using two independent approaches. Finally, we calculate the variance of these
correlation functions up to the fourth order.
