Hyper-positive definite functions I: Scalar case, branching-type stationary stochastic processes

doi:10.1016/j.jfa.2021.109266

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	Hyper-positive definite functions I: Scalar case, branching-type stationary stochastic processes
	Qiu, Yanqi 1,2; Wang, Zipeng 3
	2022
发表期刊	JOURNAL OF FUNCTIONAL ANALYSIS
ISSN	0022-1236
卷号	282 期号:1 页码:45
摘要	We propose a definition of branching-type stationary stochastic processes on rooted trees and related definitions of hyper-positivity for functions on the unit circle and functions on the set of non-negative integers. 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 hyper-positive functions 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. (C) 2021 Elsevier Inc. All rights reserved.
关键词	Hyper-positivity Positive definite kernel Herglotz-Bochner theorem Hypercontractivity
DOI	10.1016/j.jfa.2021.109266
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundation of China[NSFC Y7116335K1] ; National Natural Science Foundation of China[NSFC 11801547] ; National Natural Science Foundation of China[NSFC 11688101] ; NSFC[11601296]
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000709435800010
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/59448
专题	中国科学院数学与系统科学研究院
通讯作者	Qiu, Yanqi
作者单位	1.Wuhan Univ, Sch Math & Stat, Wuhan 430072, Hubei, Peoples R China 2.Chinese Acad Sci, AMSS, Inst Math, Beijing 100190, Peoples R China 3.Chongqing Univ, Coll Math & Stat, Chongqing 400044, Peoples R China
推荐引用方式 GB/T 7714	Qiu, Yanqi,Wang, Zipeng. Hyper-positive definite functions I: Scalar case, branching-type stationary stochastic processes[J]. JOURNAL OF FUNCTIONAL ANALYSIS,2022,282(1):45.
APA	Qiu, Yanqi,&Wang, Zipeng.(2022).Hyper-positive definite functions I: Scalar case, branching-type stationary stochastic processes.JOURNAL OF FUNCTIONAL ANALYSIS,282(1),45.
MLA	Qiu, Yanqi,et al."Hyper-positive definite functions I: Scalar case, branching-type stationary stochastic processes".JOURNAL OF FUNCTIONAL ANALYSIS 282.1(2022):45.