澳门蒲京娱乐场

科学研究
报告题目:

Herglotz-Bochner Theorem for a new stochastic processes on rooted trees and its application

报告人:

邱彦奇 研究员(中国科学院数学所)

报告时间:

报告地点:

理学院东北楼二楼报告厅(209)

报告摘要:

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.