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Dilatively semistable stochastic processes

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  • Kern, Peter
  • Wedrich, Lina

Abstract

Dilative semistability extends the notion of semi-selfsimilarity for infinitely divisible stochastic processes by introducing an additional scaling in the convolution exponent. It is shown that this scaling relation is a natural extension of dilative stability and some examples of dilatively semistable processes are given. We further characterize dilatively stable and dilatively semistable processes as limits for certain rescaled aggregations of independent processes.

Suggested Citation

  • Kern, Peter & Wedrich, Lina, 2015. "Dilatively semistable stochastic processes," Statistics & Probability Letters, Elsevier, vol. 99(C), pages 101-108.
    • Handle: RePEc:eee:stapro:v:99:y:2015:i:c:p:101-108
    DOI: 10.1016/j.spl.2015.01.008
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    References listed on IDEAS

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    1. Pilipauskaitė, Vytautė & Surgailis, Donatas, 2014. "Joint temporal and contemporaneous aggregation of random-coefficient AR(1) processes," Stochastic Processes and their Applications, Elsevier, vol. 124(2), pages 1011-1035.
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    Cited by:

    1. Bhatti, T. & Kern, P., 2017. "An integral representation of dilatively stable processes with independent increments," Stochastic Processes and their Applications, Elsevier, vol. 127(1), pages 209-227.

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