## Bernoulli

• Bernoulli
• Volume 22, Number 4 (2016), 2548-2578.

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

#### 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.

#### Article information

Source
Bernoulli, Volume 22, Number 4 (2016), 2548-2578.

Dates
Revised: May 2015
First available in Project Euclid: 3 May 2016

Permanent link to this document
https://projecteuclid.org/euclid.bj/1462297689

Digital Object Identifier
doi:10.3150/15-BEJ737

Mathematical Reviews number (MathSciNet)
MR3498037

Zentralblatt MATH identifier
1347.60006

#### Citation

Bayraktar, Erhan; Munk, Alexander. An $\alpha$-stable limit theorem under sublinear expectation. Bernoulli 22 (2016), no. 4, 2548--2578. doi:10.3150/15-BEJ737. https://projecteuclid.org/euclid.bj/1462297689

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