A functional non-central limit theorem for multiple-stable processes with long-range dependence |
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| Institution: | 1. Centro Brasileiro de Pesquisas Fisicas, Rua Xavier Sigaud 150, 22290–180 Rio de Janeiro–RJ, Brazil;2. National Institute of Science Technology for Complex Systems, Rua Xavier Sigaud 150, 22290–180 Rio de Janeiro–RJ, Brazil;3. Departamento de Física Teórica II (Métodos Matemáticos de la Física), Facultad de Físicas, Universidad Complutense, 28040–Madrid, Spain;4. Instituto de Ciencias Matemáticas, C/ Nicolás Cabrera, No 13–15, 28049 Madrid, Spain;5. Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA;1. Department of Mathematics, Nazarbayev University, Astana, 010000, Kazakhstan;2. Department of Mathematics, National University of Singapore, 119076, Singapore |
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| 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. |
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| Keywords: | Multiple integral Stable regenerative set Local time Heavy-tailed distribution Long-range dependence Infinite ergodic theory |
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