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Uniqueness of the representation for $G$-martingales with finite variation


 
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1. Title Title of document Uniqueness of the representation for $G$-martingales with finite variation
 
2. Creator Author's name, affiliation, country Yongsheng Song; Chinese Academy of Sciences, Beijing; China
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) uniqueness; representation theorem; $G$-martingale; finite variation; $G$-expectation
 
3. Subject Subject classification 60G48; 60G44
 
4. Description Abstract Letting $\{\delta_n\}$ be a refining sequence of Rademacher functions on the interval $[0,T]$, we introduce a functional on processes in the $G$-expectation space by [d(K)=\limsup_n\hat{E}[\int_0^T\delta_n(s)dK_s].\] We prove that $d(K)>0$ if $K_t=\int_0^t\eta_sd\langle B\rangle_s$ with nontrivial $\eta\in M^1_G(0,T)$ and that $d(K)=0$ if $K_t=\int_0^t\eta_sds$ with $\eta\in M^1_G(0,T)$. This implies the uniqueness of the representation for $G$-martingales with finite variation, which is the main purpose of this article.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) Supported by Youth Grant of National Science Foundation (No. 11101406/A011002); the National Basic Research Program of China (973 Program) (No.2007CB814902); Key Lab of Random Complex Structures and Data Science, CAS (Grant No. 2008DP173182).
 
7. Date (YYYY-MM-DD) 2012-03-19
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/1890
 
10. Identifier Digital Object Identifier 10.1214/EJP.v17-1890
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 17
 
12. Language English=en en
 
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