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

   
@article{EJP1890,
	author = {Yongsheng Song},
	title = {Uniqueness of the representation for $G$-martingales with finite variation},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {17},
	year = {2012},
	keywords = {uniqueness; representation theorem; \$G\$-martingale;  finite variation; \$G\$-expectation},
	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.},
	pages = {no. 24, 1-15},
	issn = {1083-6489},
	doi = {10.1214/EJP.v17-1890},    
        url = {http://ejp.ejpecp.org/article/view/1890}}