Inversion of analytic characteristic functions and infinite convolutions of exponential and Laplace densities

preprint2010arXivOpen access

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.

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