Multivariate limit theorems involving short-range and long-range dependence

Murad S. Taqqu. Dept of Mathematics, Boston University

Self-similar processes with stationary increments are important because they characterize the scaling limits of sums of stationary sequences. In this talk, we review the notions of self-similarity, short and long memory, provide a partial history of the subject and introduce a broad class of self-similar processes represented by a multiple stochastic integral, called the generalized Hermite processes. We show that the normalized sumsof some nonlinear long-memory stationary sequences converges to these generalized Hermite processes.

Joint work with Shuyang Bai.