• 科學研究
    報告題目:

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

    報告人:

    邱彥奇 研究員(中國科學院數學所)

    報告時間:

    報告地點:

    理學院東北樓二樓報告廳(209)

    報告摘要:

    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.

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