Open Access
November 2016 An $\alpha$-stable limit theorem under sublinear expectation
Erhan Bayraktar, Alexander Munk
Bernoulli 22(4): 2548-2578 (November 2016). DOI: 10.3150/15-BEJ737


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.


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Erhan Bayraktar. Alexander Munk. "An $\alpha$-stable limit theorem under sublinear expectation." Bernoulli 22 (4) 2548 - 2578, November 2016.


Received: 1 January 2015; Revised: 1 May 2015; Published: November 2016
First available in Project Euclid: 3 May 2016

zbMATH: 1347.60006
MathSciNet: MR3498037
Digital Object Identifier: 10.3150/15-BEJ737

Keywords: generalized central limit theorem , partial-integro differential equations , stable distribution , Sublinear expectation

Rights: Copyright © 2016 Bernoulli Society for Mathematical Statistics and Probability

Vol.22 • No. 4 • November 2016
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