The so-called "supOU" processes, namely the superpositions of Ornstein-Uhlenbeck type processes are stationary processes for which one can specify separately the marginal distribution and the dependence structure. They can have finite or infinite variance. We study the limit behavior of integrated infinite variance supOU processes adequately normalized. Depending on the specific circumstances, the limit can be fractional Brownian motion but it can also be a process with infinite variance, a L\'evy stable process with independent increments or a stable process with dependent increments. We show that it is even possible to have infinite variance integrated supOU processes converging to processes whose moments are all finite. A number of examples are provided.

中文翻译：

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集成 supOU 流程的多方面行为：无限方差情况

所谓的“supOU”过程，即Ornstein-Uhlenbeck 类型过程的叠加是平稳过程，可以分别指定边缘分布和依赖结构。它们可以有有限或无限的方差。我们研究了充分归一化的集成无限方差 supOU 过程的极限行为。根据具体情况，极限可以是分数布朗运动，但也可以是具有无限方差的过程，具有独立增量的L'evy稳定过程或具有相关增量的稳定过程。我们表明，甚至可以将无限方差集成 supOU 过程收敛到其矩都是有限的过程。提供了许多示例。