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A functional limit theorem is established for the partial-sum process of aclass of stationary sequences which exhibit both heavy tails and long-rangedependence. The stationary sequence is constructed using multiple stochasticintegrals with heavy-tailed marginal distribution. Furthermore, the multiplestochastic integrals are built upon a large family of dynamical systems thatare ergodic and conservative, leading to the long-range dependence phenomenonof the model. The limits constitute a new class of self-similar processes withstationary increments. They are represented by multiple stable integrals, wherethe integrands involve the local times of intersections of independentstationary stable regenerative sets. The joint moments of the local times arecomputed, which play the key in the proof and are also of independent interest.

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