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

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

2010-09-08

arxiv.org/abs/1009.1543v1

Mathematics

Probability

Scientific paper

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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