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2012 Uniqueness of the representation for $G$-martingales with finite variation
Yongsheng Song
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Electron. J. Probab. 17: 1-15 (2012). DOI: 10.1214/EJP.v17-1890

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.

Citation

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Yongsheng Song. "Uniqueness of the representation for $G$-martingales with finite variation." Electron. J. Probab. 17 1 - 15, 2012. https://doi.org/10.1214/EJP.v17-1890

Information

Accepted: 19 March 2012; Published: 2012
First available in Project Euclid: 4 June 2016

zbMATH: 1244.60046
MathSciNet: MR2900465
Digital Object Identifier: 10.1214/EJP.v17-1890

Subjects:
Primary: 60G48
Secondary: 60G44

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