时间◽️：2019年11月19日(周二) 10:30-11:30
地点：中北校区理科大楼A1716报告厅
题目：Herglotz-Bochner Theorem for a new stochastic processes on rooted trees and its application
主讲人🫣👩🏼🏭：邱彦奇 中科院数学所 研究员
摘要: We propose a definition of branching-type stationary stochastic processes on rooted trees. We then obtain (1) a necessary and sufficient condition on a rooted tree for the existence of non-trivial branching-type stationary stochastic processes on it, (2) a complete criterion of the spectral measures of branching-type stationary stochastic processes in the setting of rooted homogeneous trees in terms of a variant of the classical Herglotz-Bochner Theorem, (3) a prediction theory result for branching-type stationary stochastic processes. As an unexpected application, we obtain natural hypercontractive inequalities for Hankel operators with hyper-positive symbols. This talk is based on a joint work with Zipeng WANG.