The structure of entrance laws for time-inhomogeneous Ornstein-Uhlenbeck processes with Levy noise in Hilbert spaces

doi:10.1142/S0219025721500119

CSpace

	The structure of entrance laws for time-inhomogeneous Ornstein-Uhlenbeck processes with Levy noise in Hilbert spaces
	Majid, Narges Rezvani 1; Roeckner, Michael 1,2
	2021-06-01
发表期刊	INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS
ISSN	0219-0257
卷号	24 期号:02 页码:23
摘要	This paper is about the structure of all entrance laws (in the sense of Dynkin) for time-inhomogeneous Ornstein-Uhlenbeck processes with Levy noise in Hilbert state spaces. We identify the extremal entrance laws with finite weak first moments through an explicit formula for their Fourier transforms, generalizing corresponding results by Dynkin for Wiener noise and nuclear state spaces. We then prove that an arbitrary entrance law with finite weak first moments can be uniquely represented as an integral over extremals. It is proved that this can be derived from Dynkin's seminal work "Sufficient statistics and extreme points" in Ann. Probab. 1978, which contains a purely measure theoretic generalization of the classical analytic Krein-Milman and Choquet Theorems. As an application, we obtain an easy uniqueness proof for T-periodic entrance laws in the general periodic case. A number of further applications to concrete cases are presented.
关键词	Entrance laws evolution system of measures Ornstein Uhlenbeck processes Levy processes integral representations
DOI	10.1142/S0219025721500119
收录类别	SCI
语种	英语
资助项目	DFG[SFB-701]
WOS研究方向	Mathematics ; Physics
WOS类目	Mathematics, Applied ; Quantum Science & Technology ; Physics, Mathematical ; Statistics & Probability
WOS记录号	WOS:000677513500004
出版者	WORLD SCIENTIFIC PUBL CO PTE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/59003
专题	中国科学院数学与系统科学研究院
通讯作者	Roeckner, Michael
作者单位	1.Bielefeld Univ, Bielefeld, Germany 2.Chinese Acad Sci, AMSS, Beijing, Peoples R China
推荐引用方式 GB/T 7714	Majid, Narges Rezvani,Roeckner, Michael. The structure of entrance laws for time-inhomogeneous Ornstein-Uhlenbeck processes with Levy noise in Hilbert spaces[J]. INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS,2021,24(02):23.
APA	Majid, Narges Rezvani,&Roeckner, Michael.(2021).The structure of entrance laws for time-inhomogeneous Ornstein-Uhlenbeck processes with Levy noise in Hilbert spaces.INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS,24(02),23.
MLA	Majid, Narges Rezvani,et al."The structure of entrance laws for time-inhomogeneous Ornstein-Uhlenbeck processes with Levy noise in Hilbert spaces".INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS 24.02(2021):23.