Classes of infinitely divisible distributions on R^d related to the class of selfdecomposable distributions - Mathematics > ProbabilityReport as inadecuate




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Abstract: This paper studies new classes of infinitely divisible distributions on R^d.Firstly, the connecting classes with a continuous parameter between the Jurekclass and the class of selfdecomposable distributions are revisited. Secondly,the range of the parameter is extended to construct new classes andcharacterizations in terms of stochastic integrals with respect to Levyprocesses are given. Finally, the nested subclasses of those classes arediscussed and characterized in two ways: One is by stochastic integralrepresentations and another is in terms of Levy measures.



Author: Makoto Maejima, Muneya Matsui, Mayo Suzuki

Source: https://arxiv.org/



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