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Supermartingale decomposition theorem under \(G\)-expectation. (English) Zbl 1430.60050
Summary: 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.

MSC:
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60G44 Martingales with continuous parameter
60H30 Applications of stochastic analysis (to PDEs, etc.)
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