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

DOI10.1214/16-AOP1107zbMath1381.60081arXiv1504.00935OpenAlexW2743458099MaRDI QIDQ2406558

Yanyan Li

Publication date: 5 October 2017

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1504.00935

zbMATH Keywords

functional central limit theoremself-similar processconservative flowDarling-Kac theorempointwise dual ergodicityinfinitely divisible processfractional stable motionHarris recurrent Markov chain

Mathematics Subject Classification ID

Self-similar stochastic processes (60G18) Stable stochastic processes (60G52) Functional limit theorems; invariance principles (60F17) Nonsingular (and infinite-measure preserving) transformations (37A40)

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Limit theorems for conservative flows on multiple stochastic integrals ⋮ A FINANCIAL MARKET OF A STOCHASTIC DELAY EQUATION ⋮ Self-similar stochastic processes with stationary increments as limits of particle systems ⋮ Maxima of stable random fields, nonsingular actions and finitely generated abelian groups: a survey ⋮ Random walks in doubly random scenery ⋮ Maximal moments and uniform modulus of continuity for stable random fields ⋮ Stable random fields indexed by finitely generated free groups ⋮ Limit theorems for long-memory flows on Wiener chaos ⋮ Extremal theory for long range dependent infinitely divisible processes

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