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May 2020 Limit theorems for long-memory flows on Wiener chaos
Shuyang Bai, Murad S. Taqqu
Bernoulli 26(2): 1473-1503 (May 2020). DOI: 10.3150/19-BEJ1168

Abstract

We consider a long-memory stationary process, defined not through a moving average type structure, but by a flow generated by a measure-preserving transform and by a multiple Wiener–Itô integral. The flow is described using a notion of mixing for infinite-measure spaces introduced by Krickeberg (In Proc. Fifth Berkeley Sympos. Math. Statist. and Probability (Berkeley, Calif., 1965/66), Vol. II: Contributions to Probability Theory, Part 2 (1967) 431–446 Univ. California Press). Depending on the interplay between the spreading rate of the flow and the order of the multiple integral, one can recover known central or non-central limit theorems, and also obtain joint convergence of multiple integrals of different orders.

Citation

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Shuyang Bai. Murad S. Taqqu. "Limit theorems for long-memory flows on Wiener chaos." Bernoulli 26 (2) 1473 - 1503, May 2020. https://doi.org/10.3150/19-BEJ1168

Information

Received: 1 November 2018; Revised: 1 October 2019; Published: May 2020
First available in Project Euclid: 31 January 2020

zbMATH: 07166571
MathSciNet: MR4058375
Digital Object Identifier: 10.3150/19-BEJ1168

Keywords: conservative flows , ergodic theory , Fourth moment theorem , long memory , long-range dependence

Rights: Copyright © 2020 Bernoulli Society for Mathematical Statistics and Probability

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Vol.26 • No. 2 • May 2020
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