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An \(\alpha\)-stable limit theorem under sublinear expectation. (English) Zbl 1347.60006

Authors’ 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.

MSC:

60F05 Central limit and other weak theorems
60G52 Stable stochastic processes
60E07 Infinitely divisible distributions; stable distributions
35R09 Integro-partial differential equations
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