Properties of G-martingales with finite variation and the application to G-Sobolev spaces | |
Song, Yongsheng1,2![]() | |
刊名 | STOCHASTIC PROCESSES AND THEIR APPLICATIONS
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2019-06-01 | |
卷号 | 129期号:6页码:2066-2085 |
关键词 | G-martingales with finite variation Generalized G-ito processes Unique decomposition G-Sobolev spaces |
ISSN号 | 0304-4149 |
DOI | 10.1016/j.spa.2018.07.002 |
英文摘要 | As is known, if B = (B-t)(t is an element of[0,T]) is a G-Brownian motion, a process of form integral(t)(0) eta(s)d < B >(s) - integral(t)(0) 2G(eta(s))ds, eta is an element of M-G(1)(0, T), is a non-increasing G-martingale. In this paper, we shall show that a non-increasing G-martingale cannot be form of integral(t)(0) eta(s)ds or integral(t)(0) gamma(s)d < B >(s), eta, gamma is an element of M-G(1)(0, T), which implies that the decomposition for generalized G-Ito processes is unique: For arbitrary zeta is an element of H-G(1)(0, T), eta is an element of M-G(1)(0, T) and non-increasing G-martingales K, L, if integral(t)(0) zeta(s)d B-s + integral(t)(0) eta(s)ds + K-t = L-t, t is an element of[0, T], then we have eta 0, zeta 0 and K-t = L-t. As an application, we give a characterization to the G-Sobolev spaces introduced in Peng and Song (2015). (C) 2018 Elsevier B.V. All rights reserved. |
资助项目 | NCMIS; NSFCs[11231005] ; NCMIS; NSFCs[11688101] ; Key Research Program of Frontier Sciences, CAS[QYZDB-SSW-SYS017] |
WOS研究方向 | Mathematics |
语种 | 英语 |
出版者 | ELSEVIER SCIENCE BV |
WOS记录号 | WOS:000469157100008 |
内容类型 | 期刊论文 |
源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/34788] ![]() |
专题 | 应用数学研究所 |
通讯作者 | Song, Yongsheng |
作者单位 | 1.Chinese Acad Sci, Acad Math & Syst Sci, RCSDS, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China |
推荐引用方式 GB/T 7714 | Song, Yongsheng. Properties of G-martingales with finite variation and the application to G-Sobolev spaces[J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS,2019,129(6):2066-2085. |
APA | Song, Yongsheng.(2019).Properties of G-martingales with finite variation and the application to G-Sobolev spaces.STOCHASTIC PROCESSES AND THEIR APPLICATIONS,129(6),2066-2085. |
MLA | Song, Yongsheng."Properties of G-martingales with finite variation and the application to G-Sobolev spaces".STOCHASTIC PROCESSES AND THEIR APPLICATIONS 129.6(2019):2066-2085. |
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