Integrated random processes exhibiting long tails, finite moments, and power-law spectra - art. no. 011110

A dynamical model based on a continuous addition of colored shot noises is presented. The resulting process is colored and non-Gaussian. A general exp ression for the characteristic function of the process is obtained, which, after a scaling assumption, takes on a form that is the basis of the result s derived in the rest of the paper. One of these is an expansion for the cu mulants, which are all finite, subject to mild conditions on the functions defining the process. This is in contrast with the Levy distribution-which can be obtained from our model in certain limits-which has no finite moment s. The evaluation of the spectral density and the form of the probability d ensity function in the tails of the distribution shows that the model exhib its a power-law spectrum and long tails in a natural way. A careful analysi s of the characteristic function shows that it may be separated into a part representing a Levy process together with another part representing the de viation of our model from the Levy process. This allows our process to be v iewed as a generalization of the Levy process that has finite moments.