Electronic Journal of Probability

Supermartingale decomposition theorem under $G$-expectation

Hanwu Li, Shige Peng, and Yongsheng Song

Full-text: Open access

Abstract

The objective of this paper is to establish the decomposition theorem for supermartingales under the $G$-framework. We first introduce a $g$-nonlinear expectation via a kind of $G$-BSDE and the associated supermartingales. We have shown that this kind of supermartingales has the decomposition similar to the classical case. The main ideas are to apply the property on uniform continuity of $S_G^\beta (0,T)$, the representation of the solution to $G$-BSDE and the approximation method via penalization.

Article information

Source
Electron. J. Probab., Volume 23 (2018), paper no. 50, 20 pp.

Dates
Received: 8 March 2017
Accepted: 28 April 2018
First available in Project Euclid: 1 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1527818428

Digital Object Identifier
doi:10.1214/18-EJP173

Mathematical Reviews number (MathSciNet)
MR3814244

Zentralblatt MATH identifier
06924662

Subjects
Primary: 60H10: Stochastic ordinary differential equations [See also 34F05] 60H30: Applications of stochastic analysis (to PDE, etc.)

Keywords
$G$-expectation $\mathbb{\hat {E}} ^{g}$-supermartingale $\mathbb{\hat {E}} ^{g}$-supermartingale decomposition theorem

Rights
Creative Commons Attribution 4.0 International License.

Citation

Li, Hanwu; Peng, Shige; Song, Yongsheng. Supermartingale decomposition theorem under $G$-expectation. Electron. J. Probab. 23 (2018), paper no. 50, 20 pp. doi:10.1214/18-EJP173. https://projecteuclid.org/euclid.ejp/1527818428


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