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

Shuyang Bai, Takashi Owada and Yizao Wang

Stochastic Processes and their Applications, 2020, vol. 130, issue 9, 5768-5801

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.

Keywords: Multiple integral; Stable regenerative set; Local time; Heavy-tailed distribution; Long-range dependence; Infinite ergodic theory (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.spa.2020.04.007

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