Abstract: I present a simple method for the modelling and simulation of dependent positive jump processes through a series representation. Each constituent process is represented by a series whose terms are equal to a transformation of the jump times of a standard Poisson process. The transformations are given by the inverses of the respective marginal Levy tail mass integral functions. The dependence between the various consituent processes is given by a probalistic copula for the inter-arrival times of the various standard Poisson processes.