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Symmetry groups in d-space

Author

Listed:
  • Meerschaert, Mark M.
  • Alan Veeh, Jeery

Abstract

We show that any finite-dimensional compact Lie group is isomorphic to the symmetry group of a full probability measure. The novelty of our proof is that an explicit formula for the measure and its support is given in terms of the Lie group. We also construct a full operator stable probability measure whose symmetry group has as its tangent space the tangent space of a given group. This provides a method for constructing an operator stable probability measure having a specified collection of exponents. A characterization of the compact groups of operators on a finite-dimensional space which can be the symmetry group of a full probability measure on that same space is given.

Suggested Citation

  • Meerschaert, Mark M. & Alan Veeh, Jeery, 1995. "Symmetry groups in d-space," Statistics & Probability Letters, Elsevier, vol. 22(1), pages 1-6, January.
    • Handle: RePEc:eee:stapro:v:22:y:1995:i:1:p:1-6
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    Citations

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    Cited by:

    1. Didier, Gustavo & Meerschaert, Mark M. & Pipiras, Vladas, 2018. "Domain and range symmetries of operator fractional Brownian fields," Stochastic Processes and their Applications, Elsevier, vol. 128(1), pages 39-78.
    2. Gustavo Didier & Vladas Pipiras, 2012. "Exponents, Symmetry Groups and Classification of Operator Fractional Brownian Motions," Journal of Theoretical Probability, Springer, vol. 25(2), pages 353-395, June.
    3. Cohen, Serge & Meerschaert, Mark M. & Rosinski, Jan, 2010. "Modeling and simulation with operator scaling," Stochastic Processes and their Applications, Elsevier, vol. 120(12), pages 2390-2411, December.

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