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

Erhan Bayraktar and Alexander Munk

Papers from arXiv.org

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.

Date: 2014-09, Revised 2016-06
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Published in Bernoulli 2016, Vol. 22, No. 4, 2548-2578

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