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Topological crackle of heavy-tailed moving average processes

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  • Owada, Takashi

Abstract

The main focus of this paper is topological crackle, the layered structure of annuli formed by heavy-tailed random points in Rd. In view of extreme value theory, we study the topological crackle generated by a heavy-tailed discrete-time moving average process. Because of the clustering effect of a moving average process, various topological cycles are produced consecutively in time in the layers of the crackle. We establish the limit theorems for the Betti numbers, a basic quantifier of topological cycles. The Betti number converges to the sum of stochastic integrals, some of which induce multiple cycles because of the clustering effect.

Suggested Citation

  • Owada, Takashi, 2019. "Topological crackle of heavy-tailed moving average processes," Stochastic Processes and their Applications, Elsevier, vol. 129(12), pages 4965-4997.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:12:p:4965-4997
    DOI: 10.1016/j.spa.2018.12.017
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    References listed on IDEAS

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    Cited by:

    1. Bonnet, Gilles & Hirsch, Christian & Rosen, Daniel & Willhalm, Daniel, 2023. "Limit theory of sparse random geometric graphs in high dimensions," Stochastic Processes and their Applications, Elsevier, vol. 163(C), pages 203-236.

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