@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}, pages = {605--630}, publisher = {Elsevier}, volume = {41}, number = {3}, year = {2005}, doi = {10.1016/j.anihpb.2004.12.002}, zbl = {1071.60049}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.anihpb.2004.12.002/} }
TY - JOUR AU - Peng, Shige AU - Xu, Mingyu TI - The smallest $g$-supermartingale and reflected BSDE with single and double ${L}^{2}$ obstacles JO - Annales de l'I.H.P. Probabilités et statistiques PY - 2005 SP - 605 EP - 630 VL - 41 IS - 3 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.anihpb.2004.12.002/ DO - 10.1016/j.anihpb.2004.12.002 LA - en ID - AIHPB_2005__41_3_605_0 ER -
%0 Journal Article %A Peng, Shige %A Xu, Mingyu %T The smallest $g$-supermartingale and reflected BSDE with single and double ${L}^{2}$ obstacles %J Annales de l'I.H.P. Probabilités et statistiques %D 2005 %P 605-630 %V 41 %N 3 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.anihpb.2004.12.002/ %R 10.1016/j.anihpb.2004.12.002 %G en %F 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, Volume 41 (2005) no. 3, pp. 605-630. doi : 10.1016/j.anihpb.2004.12.002. http://archive.numdam.org/articles/10.1016/j.anihpb.2004.12.002/
[1] Dynkin games, in: Lecture Notes in Control and Inform. Sci., vol. 43, Springer, Berlin, 1982, pp. 23-42. | MR
, , ,[2] Non-linear variational inequalities and differential games with stopping times, J. Funct. Anal. 16 (1974) 305-352. | MR | Zbl
, ,[3] Sur un probleme de Dynkin, Z. Wahrsch. Verw. Gebiete 39 (1977) 31-53. | MR | Zbl
,[4] Backward stochastic differential equations with reflection and Dynkin games, Ann. Probab. 24 (4) (1996) 2024-2056. | MR | Zbl
, ,[5] Filtration-consistent nonlinear expectations and related g-expectations, Probab. Theory Related Fields 123 (2002) 1-27. | MR | Zbl
, , , ,[6] Probabilités et Potentiel, I-IV, Hermann, Paris, 1975. | MR | Zbl
, ,[7] Probabilités et Potentiel, V-VIII, Hermann, Paris, 1980. | MR | Zbl
, ,[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 | Zbl
,[10] Reflected solutions of backward SDE and related obstacle problems for PDEs, Ann. Probab. 25 (2) (1997) 702-737. | MR | Zbl
, , , , ,[11] Backward stochastic differential equations in finance, Math. Finance 7 (1997) 1-71. | MR | Zbl
, , ,[12] Reflected BSDE's with discontinuous barrier and application, Stochastics Stochastics Rep. 74 (3-4) (2002) 571-596. | MR | Zbl
,[13] Reflected BSDE's and mixed game problem, Stochastics Process. Appl. 85 (2000) 177-188. | MR | Zbl
, ,[14] Double barrier backward SDEs with continuous coefficient, in: , (Eds.), Pitman Res. Notes Math. Ser., vol. 364, 1997, pp. 161-171. | MR | Zbl
, , ,[15] Brownian Motion and Stochastic Calculus, Springer, New York, 1991. | MR | Zbl
, ,[16] J.-P. Lepeltier, M. Xu, Penalization method for reflected backward stochastic differential equations with one r.c.l.l. barrier, Preprint, 2004. | MR
[17] Dynkin games and martingale methods, Stochastics 13 (1984) 213-228. | MR | Zbl
,[18] Discrete-Parameter Martingales, North-Holland, Amsterdam, 1975. | MR | Zbl
,[19] Adapted solutions of backward stochastic differential equations, Systems Control Lett. 14 (1990) 51-61. | MR | Zbl
, ,[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 | Zbl
,[21] Monotonic limit theory of BSDE and nonlinear decomposition theorem of Doob-Meyer's type, Probab. Theory Related Fields 113 (1999) 473-499. | MR | Zbl
,[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 | Zbl
,[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 | Zbl
,Cited by Sources: