Functional central limit theorem for negatively dependent heavy-tailed stationary infinitely divisible processes generated by conservative flows
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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.
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Jung's research was partially supported by NSA grant H98230-14-1-0144. Owada's research was partially supported by URSAT, ERC Advanced Grant 320422. Samorodnitsky's research was partially supported by the ARO
grant W911NF-12-10385 at Cornell University
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2015-04-06
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Keywords
infinitely divisible proces; conservative flow; Harris recurrent Markov chain; functional central limit theorem; self-similar process; pointwise dual ergodicity; Darling-Kac theorem; fractional stable motion
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technical report