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An $\alpha$-stable limit theorem under sublinear expectation

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  • Erhan Bayraktar
  • Alexander Munk

Abstract

For $\alpha\in (1,2)$, we present a generalized central limit theorem for $\alpha$-stable random variables under sublinear expectation. The foundation of our proof is an interior regularity estimate for partial integro-differential equations (PIDEs). A classical generalized central limit theorem is recovered as a special case, provided a mild but natural additional condition holds. Our approach contrasts with previous arguments for the result in the linear setting which have typically relied upon tools that are non-existent in the sublinear framework, for example, characteristic functions.

Suggested Citation

  • Erhan Bayraktar & Alexander Munk, 2014. "An $\alpha$-stable limit theorem under sublinear expectation," Papers 1409.7960, arXiv.org, revised Jun 2016.
    • Handle: RePEc:arx:papers:1409.7960
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    References listed on IDEAS

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    5. Ren, Liying, 2013. "On representation theorem of sublinear expectation related to G-Lévy process and paths of G-Lévy process," Statistics & Probability Letters, Elsevier, vol. 83(5), pages 1301-1310.
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