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The structure of the exponents and symmetries of an operator stable measure

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Abstract

A series of decomposition theorems are presented, leading to a description of the structure of the exponents and symmetries of an arbitrary operator stable measure. An example of a full operator stable measure with a one parameter group as its symmetry group is presented. Connections between the structure results and the generalized domain of attraction problem and tail behavior of the operator stable measure are described.

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Authors and Affiliations

  1. Albion College, Albion, USA

    Mark M. Meerschaert

  2. Auburn University, Auburn, USA

    Jerry Alan Veeh

Authors
  1. Mark M. Meerschaert
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  2. Jerry Alan Veeh
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Partially supported by National Science Foundation grant DMS-89-23068 and DMS-91-03131.

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Meerschaert, M.M., Veeh, J.A. The structure of the exponents and symmetries of an operator stable measure. J Theor Probab 6, 713–726 (1993). https://doi.org/10.1007/BF01049173

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  • DOI: https://doi.org/10.1007/BF01049173

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