@article{AIHPB_2005__41_3_605_0,
author = {Peng, Shige and Xu, Mingyu},
title = {The smallest $g$-supermartingale and reflected BSDE with single and double ${L}^{2}$ obstacles},
journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
volume = {41},
year = {2005},
pages = {605-630},
doi = {10.1016/j.anihpb.2004.12.002},
zbl = {1071.60049},
language = {en},
url = {http://dml.mathdoc.fr/item/AIHPB_2005__41_3_605_0}
}
Peng, Shige; Xu, Mingyu. The smallest $g$-supermartingale and reflected BSDE with single and double ${L}^{2}$ obstacles. Annales de l'I.H.P. Probabilités et statistiques, Tome 41 (2005) pp. 605-630. doi : 10.1016/j.anihpb.2004.12.002. http://gdmltest.u-ga.fr/item/AIHPB_2005__41_3_605_0/
[1] , , , Dynkin games, in: Lecture Notes in Control and Inform. Sci., vol. 43, Springer, Berlin, 1982, pp. 23-42. | MR 814103
[2] , , Non-linear variational inequalities and differential games with stopping times, J. Funct. Anal. 16 (1974) 305-352. | MR 354049 | Zbl 0297.90120
[3] , Sur un probleme de Dynkin, Z. Wahrsch. Verw. Gebiete 39 (1977) 31-53. | MR 444218 | Zbl 0336.60069
[4] , , Backward stochastic differential equations with reflection and Dynkin games, Ann. Probab. 24 (4) (1996) 2024-2056. | MR 1415239 | Zbl 0876.60031
[5] , , , , Filtration-consistent nonlinear expectations and related g-expectations, Probab. Theory Related Fields 123 (2002) 1-27. | MR 1906435 | Zbl 1007.60057
[6] , , Probabilités et Potentiel, I-IV, Hermann, Paris, 1975. | MR 488194 | Zbl 0323.60039
[7] , , Probabilités et Potentiel, V-VIII, Hermann, Paris, 1980. | MR 488194 | Zbl 0464.60001
[8] , , Theorems and Problems in Markov Processes, Plenum Press, New York, 1968.
[9] , Les aspects probabilistes du contrôle stochastique, in: Ecole d'été de Saint-Flour, 1979, Lecture Notes in Math., vol. 876, Springer, Berlin, 1981, pp. 73-238. | MR 637471 | Zbl 0472.60002
[10] , , , , , Reflected solutions of backward SDE and related obstacle problems for PDEs, Ann. Probab. 25 (2) (1997) 702-737. | MR 1434123 | Zbl 0899.60047
[11] , , , Backward stochastic differential equations in finance, Math. Finance 7 (1997) 1-71. | MR 1434407 | Zbl 0884.90035
[12] , Reflected BSDE's with discontinuous barrier and application, Stochastics Stochastics Rep. 74 (3-4) (2002) 571-596. | MR 1943580 | Zbl 1015.60057
[13] , , Reflected BSDE's and mixed game problem, Stochastics Process. Appl. 85 (2000) 177-188. | MR 1731020 | Zbl 0999.91005
[14] , , , Double barrier backward SDEs with continuous coefficient, in: , (Eds.), Pitman Res. Notes Math. Ser., vol. 364, 1997, pp. 161-171. | MR 1752681 | Zbl 0887.60065
[15] , , Brownian Motion and Stochastic Calculus, Springer, New York, 1991. | MR 1121940 | Zbl 0734.60060
[16] J.-P. Lepeltier, M. Xu, Penalization method for reflected backward stochastic differential equations with one r.c.l.l. barrier, Preprint, 2004. | MR 2185610
[17] , Dynkin games and martingale methods, Stochastics 13 (1984) 213-228. | MR 762817 | Zbl 0569.60050
[18] , Discrete-Parameter Martingales, North-Holland, Amsterdam, 1975. | MR 402915 | Zbl 0345.60026
[19] , , Adapted solutions of backward stochastic differential equations, Systems Control Lett. 14 (1990) 51-61. | MR 1037747 | Zbl 0692.93064
[20] , Backward SDE and related g-expectation, in: , (Eds.), Backward Stochastic Differential Equations, Pitman Res. Notes Math. Ser., vol. 364, 1997, pp. 141-159. | MR 1752680 | Zbl 0892.60066
[21] , Monotonic limit theory of BSDE and nonlinear decomposition theorem of Doob-Meyer's type, Probab. Theory Related Fields 113 (1999) 473-499. | MR 1717527 | Zbl 0953.60059
[22] , Nonlinear expectations, nonlinear evaluations and risk measures, in: Lecture Notes in CIME-EMS, Bressanone, Italy, July, 2003, Lecture Notes in Math., Springer, 2004. | MR 2113723 | Zbl 02144817
[23] S. Peng, Dynamical consistent nonlinear evaluations and expectations, Preprint, 2003.
[24] , Studies in the Theory of the Random Processes, Addison-Wesley, New York, 1965. | MR 185620 | Zbl 0146.37701