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Journal of Theoretical Probability

, Volume 29, Issue 1, pp 292–306 | Cite as

Strong Mixing and Operator-Selfdecomposability

  • Richard C. Bradley
  • Zbigniew J. Jurek
Article
  • 143 Downloads

Abstract

For nonstationary, strongly mixing sequences of random variables taking their values in a finite-dimensional Euclidean space, with the partial sums being normalized via matrix multiplication, with certain standard conditions being met (an “infinitesimality” assumption, and a restriction to “full” distributions), the possible limit distributions are precisely the operator-self-decomposable laws.

Keywords

Strong mixing Operator self-decomposability Urbanik semigroup 

Mathematics Subject Classification

Primary 60B10 60E07 60F05 Secondary 15A16 20M20 

Notes

Acknowledgments

The authors thank the referee and the associate editor for their helpful comments, which improved the exposition.

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of MathematicsIndiana UniversityBloomingtonUSA
  2. 2.Institute of MathematicsUniversity of WrocławWrocławPoland

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