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Backward stochastic differential equations with jumps and related nonlinear expectations. (English) Zbl 1110.60062

Consider real-valued backward stochastic differential equations with jumps together with their applications to nonlinear expectations, where the underlying filtration is generated by a Brownian motion and a Poisson random measure. The author studies comparison theorems and monotonicity of solutions of those equations. Additivity, inverse theorems, martingale-properties, and decomposition theorems are investigated among further properties of its solutions. The notions of \(f\)-expectations and nonlinear expectations are introduced. This paper can be understood in conjunction with the work of E. Pardoux and S. G. Peng [Syst. Control Lett. 14 , No. 1, 55–61 (1990; Zbl 0692.93064)].

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H30 Applications of stochastic analysis (to PDEs, etc.)

Citations:

Zbl 0692.93064
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References:

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