Optimal Holder continuity and hitting probabilities for SPDEs with rough fractional noises
文献类型：期刊论文
| 作者 | Hong, Jialin1,2; Liu, Zhihui3; Sheng, Derui1,2 |
| 刊名 | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
 |
| 出版日期 | 2022-08-01 |
| 卷号 | 512期号:1页码:21 |
| 关键词 | Stochastic partial differential equation Fractional Brownian sheet Hurst index H < 1/2 Holder exponent Hitting probability |
| ISSN号 | 0022-247X |
| DOI | 10.1016/j.jmaa.2022.126125 |
| 英文摘要 | 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. |
| 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 |
| 语种 | 英语 |
| WOS记录号 | WOS:000821051500018 |
| 出版者 | ACADEMIC PRESS INC ELSEVIER SCIENCE |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/61121]  |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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