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Filtered Poisson processes are often used as reference models forintermittent fluc- tuations in physical systems. Such a process is hereextended by adding a noise term, either as a purely additive term to theprocess or as a dynamical term in a stochastic differential equation. Thelowest order moments, probability density function, auto-correlation functionand power spectral density are derived and used to identify and compare theeffects of the two different noise terms. Monte-Carlo studies of synthetic timeseries are used to investigate the accuracy of model pa- rameter estimation andto identify methods for distinguishing the noise types. It is shown that theprobability density function and the three lowest order moments provideaccurate estimations of the parameters, but are unable to separate the noisetypes. The auto-correlation function and the power spectral density alsoprovide methods for estimating the model parameters, as well as being capableof identifying the noise type. The number of times the signal crosses aprescribed threshold level in the positive direction also promises to be ableto differentiate the noise type.

Statistical properties of a filtered Poisson process with additive random noise: Distributions, correlations and moment estimation