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.

Published at http://dx.doi.org/10.3150/15-BEJ737 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

References in corpus (4)

• A New Central Limit Theorem under Sublinear Expectations
• Regularity for parabolic integro-differential equations with very irregular kernels
• $G$-martingale representation in the $G$-L'evy setting
• A note on characterizations of G-normal distribution

Cited by in corpus (1)

• Lindeberg's central limit theorems for martingale like sequences under sub-linear expectations