An alpha-stable limit theorem under sublinear expectation

作者：Bayraktar Erhan^*; Munk Alexander^*

来源：Bernoulli, 2016, 22(4): 2548-2578.

DOI：10.3150/15-BEJ737

• generalized central limit theorem
• partial-integro differential equations
• stable distribution
• sublinear expectation

For alpha is an element of (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.

• 出版日期2016-11