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. The joint moments of the local times are computed, which play the key in the proof and are also of independent interest.

中文翻译：

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具有长程相关性的多稳定过程的函数非中心极限定理

建立了一类具有重尾和长程相关性的平稳序列的部分和过程的泛函极限定理。平稳序列是使用具有重尾边缘分布的多个随机积分构建的。此外，多重随机积分建立在一个大家族的遍历和保守的动力系统上，导致模型的长期依赖现象。极限构成了一类新的具有平稳增量的自相似过程。它们由多个稳定积分表示，其中被积函数涉及独立平稳稳定再生集的交点的局部时间。计算本地时间的联合矩，这在证明中起关键作用，也具有独立的兴趣。