Inversion of analytic characteristic functions and infinite convolutions of exponential and Laplace densities (1009.1543v1)

Abstract: We prove that certain quotients of entire functions are characteristic functions. Under some conditions, the probability measure corresponding to a characteristic function of that type has a density which can be expressed as a generalized Dirichlet series, which in turn is an infinite linear combination of exponential or Laplace densities. These results are applied to several examples.