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A functional non-central limit theorem for multiple-stable processes with long-range dependence

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  • Bai, Shuyang
  • Owada, Takashi
  • Wang, Yizao

Abstract

A functional limit theorem is established for the partial-sum process of a class of stationary sequences which exhibit both heavy tails and long-range dependence. The stationary sequence is constructed using multiple stochastic integrals with heavy-tailed marginal distribution. Furthermore, the multiple stochastic integrals are built upon a large family of dynamical systems that are ergodic and conservative, leading to the long-range dependence phenomenon of the model. The limits constitute a new class of self-similar processes with stationary increments. They are represented by multiple stable integrals, where the integrands involve the local times of intersections of independent stationary stable regenerative sets.

Suggested Citation

  • Bai, Shuyang & Owada, Takashi & Wang, Yizao, 2020. "A functional non-central limit theorem for multiple-stable processes with long-range dependence," Stochastic Processes and their Applications, Elsevier, vol. 130(9), pages 5768-5801.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:9:p:5768-5801
    DOI: 10.1016/j.spa.2020.04.007
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    References listed on IDEAS

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    1. Bai, Shuyang & Taqqu, Murad S., 2014. "Generalized Hermite processes, discrete chaos and limit theorems," Stochastic Processes and their Applications, Elsevier, vol. 124(4), pages 1710-1739.
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    Cited by:

    1. Shuyang Bai, 2022. "Limit Theorems for Conservative Flows on Multiple Stochastic Integrals," Journal of Theoretical Probability, Springer, vol. 35(2), pages 917-948, June.
    2. Shuyang Bai & He Tang, 2024. "Joint Sum-and-Max Limit for a Class of Long-Range Dependent Processes with Heavy Tails," Journal of Theoretical Probability, Springer, vol. 37(3), pages 1958-1987, September.

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