Optimal Holder continuity and hitting probabilities for SPDEs with rough fractional noises

doi:10.1016/j.jmaa.2022.126125

CSpace

	Optimal Holder continuity and hitting probabilities for SPDEs with rough fractional noises
	Hong, Jialin 1,2; Liu, Zhihui 3; Sheng, Derui 1,2
	2022-08-01
发表期刊	JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
ISSN	0022-247X
卷号	512 期号:1 页码:21
摘要	We investigate the optimal Holder continuity and hitting probabilities for systems of stochastic heat equations and stochastic wave equations driven by an additive fractional Brownian sheet with temporal index 1/2 and spatial index H <= 1/2. Using stochastic calculus for fractional Brownian motion, we prove that these systems are well-posed and the solutions are Holder continuous. Furthermore, the optimal Holder exponents are obtained, which is the first result, as far as we knew, on the optimal Holder continuity of SHEs and SWEs driven by fractional Brownian sheet that is rough in space. Based on this sharp regularity, we obtain lower and upper bounds of hitting probabilities of the solutions in terms of Bessel-Riesz capacity and Hausdorff measure, respectively. (C) 2022 Elsevier Inc. All rights reserved.
关键词	Stochastic partial differential equation Fractional Brownian sheet Hurst index H < 1/2 Holder exponent Hitting probability
DOI	10.1016/j.jmaa.2022.126125
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundation of China[11971470] ; National Natural Science Foundation of China[11926417] ; National Natural Science Foundation of China[12101296] ; Southern University of Science and Technology fund[Y01286232]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000821051500018
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/61122
专题	中国科学院数学与系统科学研究院
通讯作者	Sheng, Derui
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Southern Univ Sci & Technol, Dept Math, Shenzhen 518055, Peoples R China
推荐引用方式 GB/T 7714	Hong, Jialin,Liu, Zhihui,Sheng, Derui. Optimal Holder continuity and hitting probabilities for SPDEs with rough fractional noises[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS,2022,512(1):21.
APA	Hong, Jialin,Liu, Zhihui,&Sheng, Derui.(2022).Optimal Holder continuity and hitting probabilities for SPDEs with rough fractional noises.JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS,512(1),21.
MLA	Hong, Jialin,et al."Optimal Holder continuity and hitting probabilities for SPDEs with rough fractional noises".JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 512.1(2022):21.