We study the partial sum of stationary stochastic integral infinitely divisible processes with regularly varying local Levy measure.
It is believed that memory properties of the processes are closely related to the ergodic theoretical properties of their flow. We consider the processes generated by conservative null flows. This process can be viewed as having a longer memory than commonly used mixing-like weakly dependent counterparts. Under the condition that the flow has a Darling-Kac set, we establish the functional central limit theorem, where the limit process gives us a new class of self similar stable processes with stationary increments. The weak limits also have continuous sample paths and are characterized by the Mittag-Leffler process with order determined by the corresponding Darling-Kac set. (This is a joint work with Professor G. Samorodnitsky at Cornell University. )
*** Talk will be given in Japanese. ***
※本セミナーは、機構長裁量経費による減災に向けての緊急プロジェクト「システム・レジリエンス学の創成にむけたフィージビリティ・スタディ」 からの援助を受けています。