<p>An expression for the probability generating functional of photon arrival processes in fluorescence fluctuation spectroscopy systems assuming an arbitrary fluorescence intensity over the observation interval is obtained. The use of generating functionals generalizes the theory of photon counting distribution analysis methods based on the application of photon counts generating functions and opens the possibility of analyzing systems with nonstationary intensity over the observation interval. Expressions for the process intensity and the probability of obtaining a certain number of photocounts per observation interval are found. Based on the obtained expressions, a method for estimating the concentration of fluorescent molecules with an arbitrary fluorescence intensity is developed. The method is applicable for both single-photon and two-photon excitation and does not depend on the form of the brightness profile function.</p>