A stationary sequence is said to have long memory, if the dependence decays slowly so that some non-standard scaling limit arises. Recently, there has been considerable interest in a class of long-memory models involving conservative flows in infinite ergodic theory. In this talk, we shall discuss a class of stationary sequences constructed using conservative flows as well as multiple stochastic integrals. In particular, we will introduce some recent progress on the limit theorems for sums of such sequences. The talk is based on joint works with Takashi Owada, Murad Taqqu, and Yizao Wang.

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