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February 2015 Functional central limit theorem for heavy tailed stationary infinitely divisible processes generated by conservative flows
Takashi Owada, Gennady Samorodnitsky
Ann. Probab. 43(1): 240-285 (February 2015). DOI: 10.1214/13-AOP899

Abstract

We establish a new class of functional central limit theorems for partial sum of certain symmetric stationary infinitely divisible processes with regularly varying Lévy measures. The limit process is a new class of symmetric stable self-similar processes with stationary increments that coincides on a part of its parameter space with a previously described process. The normalizing sequence and the limiting process are determined by the ergodic-theoretical properties of the flow underlying the integral representation of the process. These properties can be interpreted as determining how long the memory of the stationary infinitely divisible process is. We also establish functional convergence, in a strong distributional sense, for conservative pointwise dual ergodic maps preserving an infinite measure.

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Takashi Owada. Gennady Samorodnitsky. "Functional central limit theorem for heavy tailed stationary infinitely divisible processes generated by conservative flows." Ann. Probab. 43 (1) 240 - 285, February 2015. https://doi.org/10.1214/13-AOP899

Information

Published: February 2015
First available in Project Euclid: 12 November 2014

zbMATH: 1320.60090
MathSciNet: MR3298473
Digital Object Identifier: 10.1214/13-AOP899

Subjects:
Primary: 60F17 , 60G18
Secondary: 37A40 , 60G52

Keywords: central limit theorem , conservative flow , Darling–Kac theorem , infinitely divisible process , pointwise dual ergodicity , self-similar process

Rights: Copyright © 2015 Institute of Mathematical Statistics

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Vol.43 • No. 1 • February 2015
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