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We prove a functional central limit theorem for partial sums of symmetricstationary long range dependent heavy tailed infinitely divisible processeswith a certain type of negative dependence. Previously only positive dependencecould be treated. The negative dependence involves cancellations of theGaussian second order. This leads to new types of limiting processes involvingstable random measures, due to heavy tails, Mittag-Leffler processes, due tolong memory, and Brownian motions, due to the Gaussian second ordercancellations.

Functional central limit theorem for negatively dependent heavy-tailed stationary infinitely divisible processes generated by conservative flows