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Reflected backward doubly stochastic differential equations driven by a Lévy process. (English. Abridged French version) Zbl 1188.60031
Summary: We prove the existence and uniqueness of a solution for reflected backward doubly stochastic differential equations (RBDSDEs) driven by Teugels martingales associated with a Lévy process, in which the obstacle process is right continuous with left limits (càdlàg), via Snell envelope and the fixed point theorem.

MSC:
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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[1] Bahlali, K.; Hassani, M.; Mansouri, B.; Mrhardy, N., One barrier reflected backward doubly stochastic differential equations with continuous generator, C. R. acad. sci. Paris, ser. I, 347, 1201-1206, (2009) · Zbl 1176.60041
[2] Hamadène, S., Reflected BSDEs with discontinuous barrier and applications, Stochastics stochastics rep., 74, 571-596, (2002) · Zbl 1015.60057
[3] Hamadène, S.; Ouknine, Y., Reflected backward stochastic differential equations with jumps and random obstacle, Electron. J. probab., 8, 1-20, (2003) · Zbl 1015.60051
[4] He, S.; Wang, J.; Yan, J., Semimartingale and stochastic analysis, (1995), Scientific Press Beijing
[5] Lepeltier, J.-P.; Xu, M., Penalization method for reflected backward stochastic differential equations with one r.c.l.l. barrier, Statist. probab. lett., 75, 58-66, (2005) · Zbl 1082.60059
[6] Nualart, D.; Schoutens, W., Chaotic and predictable representation for Lévy processes, Stochastic process. appl., 90, 109-122, (2000) · Zbl 1047.60088
[7] Ren, Y.; Hu, L., Reflected backward stochastic differential equation driven by Lévy processes, Statist. probab. lett., 77, 1559-1566, (2007) · Zbl 1128.60048
[8] Ren, Y.; Lin, A.; Hu, L., Stochastic PDIEs and backward doubly stochastic differential equations driven by Lévy processes, J. comput. appl. math., 223, 901-907, (2009) · Zbl 1154.60336
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