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Properties of G-martingales with finite variation and the application to G-Sobolev spaces
Song, Yongsheng1,2
2019-06-01
Source PublicationSTOCHASTIC PROCESSES AND THEIR APPLICATIONS
ISSN0304-4149
Volume129Issue:6Pages:2066-2085
AbstractAs 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.
KeywordG-martingales with finite variation Generalized G-ito processes Unique decomposition G-Sobolev spaces
DOI10.1016/j.spa.2018.07.002
Language英语
Funding ProjectNCMIS; NSFCs[11231005] ; NCMIS; NSFCs[11688101] ; Key Research Program of Frontier Sciences, CAS[QYZDB-SSW-SYS017]
WOS Research AreaMathematics
WOS SubjectStatistics & Probability
WOS IDWOS:000469157100008
PublisherELSEVIER SCIENCE BV
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/34789
Collection应用数学研究所
Corresponding AuthorSong, Yongsheng
Affiliation1.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
Recommended Citation
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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