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Spectral decomposition for operator self-similar processes and their generalized domains of attraction

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  • Meerschaert, Mark M.
  • Scheffler, Hans-Peter

Abstract

A stochastic process on a finite-dimensional real vector space is operator-self-similar if a linear time change produces a new process whose distributions scale back to those of the original process, where we allow scaling by a family of affine linear operators. We prove a spectral decomposition theorem for these processes, and for processes with these scaling limits. This decomposition reduces the study of these processes to the case where the growth behavior over time is essentially uniform in all radial directions.

Suggested Citation

  • Meerschaert, Mark M. & Scheffler, Hans-Peter, 1999. "Spectral decomposition for operator self-similar processes and their generalized domains of attraction," Stochastic Processes and their Applications, Elsevier, vol. 84(1), pages 71-80, November.
    • Handle: RePEc:eee:spapps:v:84:y:1999:i:1:p:71-80
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    References listed on IDEAS

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    1. Maejima, Makoto & Mason, J. David, 1994. "Operator-self-similar stable processes," Stochastic Processes and their Applications, Elsevier, vol. 54(1), pages 139-163, November.
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    Cited by:

    1. 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.

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