\(G_\Gamma\)-expectations and the related nonlinear Doob-Meyer decomposition theorem. (English) Zbl 1200.60046
Tang, Shanjian (ed.) et al., Control theory and related topics. In memory of Professor Xunjing Li, Fudan, China, June 3–5, 2005. Hackensack, NJ: World Scientific (ISBN 978-981-270-582-2/hbk). 122-140 (2007).
Summary: We define a nonlinear expectation via the BSDE with constraint (BSDE with singular coefficient), then we introduce definitions of super and sub martingale under this nonlinear expectation and prove their nonlinear Doob-Meyer type decomposition.
For the entire collection see [Zbl 1130.93008].
For the entire collection see [Zbl 1130.93008].
MSC:
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 60G48 | Generalizations of martingales |
| 60G20 | Generalized stochastic processes |
