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

TL;DR

This paper establishes a functional central limit theorem for negatively dependent, heavy-tailed, stationary infinitely divisible processes, revealing new limiting behaviors involving stable measures, Mittag-Leffler processes, and Brownian motion.

Contribution

It extends the functional central limit theorem to include negatively dependent processes, previously only positive dependence was addressed.

Findings

New limit processes involving stable random measures and Mittag-Leffler processes

Negative dependence leads to cancellations affecting the Gaussian second order

Results applicable to long-range dependent heavy-tailed processes

Abstract

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