確率論セミナー


2020/10/27(Tue)

16:30--18:00 オンラインで開催

永幡 幸生

新潟大学

On functional central limit theorem for tagged particle dynamics in stochastic ranking process with space dependent intensities

In this talk, we consider a "parabolic" scaling limit of tagged particle dynamics and that of empirical measure of the position of particles for stochastic ranking process with space-time dependent intensities. A stochastic ranking process is introduced by K.Hattori and T.Hattori in order to explain the reasons why some typical curves is observed in time evolution of ranking of books in online bookstores. T.Hattori characterize this typical curve by means of a "hyperbolic" scaling limit of tagged particle dynamics. He also give a "hyperbolic" scaling limit of empirical measure of the position of particles. We obtained a sum of diffusion process as a "parabolic" scaling limit of tagged particle dynamics. We also obtained a generalized Ornstein-Uhlenbeck process for a "parabolic" scaling limit of empirical measure of the position of particles. *本セミナーは Zoom を用いて行われます。 参加を希望される方は塩沢(shiozawa "at" math.sci.osaka-u.ac.jp)まで お問い合わせ下さい。