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Decomposition of multivariate infinitely divisible characteristic functions with absolutely continuous Poisson spectral measures
Authors:Shigeru Mase
Institution:Department of Information Sciences, Tokyo Institute of Technology Japan
Abstract:We shall consider the decomposition problem of multivariate infinitely divisible characteristic functions which have no Gaussian component and have absolutely continuous Poisson spectral measures. Under the condition that A = {x;f(x) > 0} is open, where f is the density of spectral measure, we shall show that a known sufficient condition for the membership of the class I0m (i.e., infinitely divisible characteristic functions having only infinitely divisible factors) is also necessary.
Keywords:Decomposition  multivariate laws  infinitely divisible  absolutely continuous Poisson spectral measure  indecompossable factor
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