Nonlinear Doob-Meyer decomposition with jumps.
A nonlinear Doob-Meyer decomposition theorem and the smallest \(g\)-supersolution for the BSDE driven by Brownian motion are stated in work by \textit{S. Peng} [Probab. Theory Relat. Fields 113, No. 4, 473--499 (1999; Zbl 0953.60059)]. In this paper, the author considers the nonlinear Doob-Meyer decomposition theorem for the BSDE driven by both Brownian motion and the Poisson point process. To do this, the comparison theorem and the limit theorem of \(g\)-supersolution is discussed, and the concept of \(g\)-supermartingale is introduced. We note, that the limit theorem of \(g\)-supersolution began to be considered since the original work by \textit{N. El Karui} and \textit{M.-C. Quenez} [SIAM J. Control Optimization 33, 29--66 (1995; Zbl 0831.90010)].
scientific article; zbMATH DE number 1921178