An $α$-Stable Limit Theorem Under Sublinear Expectation

Erhan Bayraktar, Alexander Munk

Published 2014-09-28Version 1

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 nonexistent in the sublinear framework, e.g., characteristic functions.