  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.
