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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 729636, 7 pages
Reflected Backward Stochastic Differential Equations Driven by Countable Brownian Motions
1Laboratory of Intelligent Information Processing, Suzhou University, Anhui 234000, China
2Department of Mathematics, Suzhou University, Anhui 234000, China
Received 16 June 2013; Accepted 15 September 2013
Academic Editor: Lotfollah Najjar
Copyright © 2013 Pengju Duan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- E. Pardoux and S. G. Peng, “Adapted solution of a backward stochastic differential equation,” Systems & Control Letters, vol. 14, no. 1, pp. 55–61, 1990.
- X. Mao, “Adapted solutions of backward stochastic differential equations with non-Lipschitz coefficients,” Stochastic Processes and their Applications, vol. 58, no. 2, pp. 281–292, 1995.
- K. Bahlali, E. H. Essaky, M. Hassani, and E. Pardoux, “Existence, uniqueness and stability of backward stochastic differential equations with locally monotone coefficient,” Comptes Rendus Mathématique, vol. 335, no. 9, pp. 757–762, 2002.
- P. Briand, B. Delyon, Y. Hu, E. Pardoux, and L. Stoica, “ solutions of backward stochastic differential equations,” Stochastic Processes and their Applications, vol. 108, no. 1, pp. 109–129, 2003.
- J. P. Lepeltier and J. S. Martin, “Backward stochastic differential equations with continuous coefficient,” Statistics & Probability Letters, vol. 14, pp. 55–514, 1997.
- G. Jia, “A class of backward stochastic differential equations with discontinuous coefficients,” Statistics & Probability Letters, vol. 78, no. 3, pp. 231–237, 2008.
- N. El Karoui, S. Peng, and M. C. Quenez, “Backward stochastic differential equations in finance,” Mathematical Finance, vol. 7, no. 1, pp. 1–71, 1997.
- S. Hamadene and J.-P. Lepeltier, “Zero-sum stochastic differential games and backward equations,” Systems & Control Letters, vol. 24, no. 4, pp. 259–263, 1995.
- E. Pardoux and S. G. Peng, “Backward doubly stochastic differential equations and systems of quasilinear SPDEs,” Probability Theory and Related Fields, vol. 98, no. 2, pp. 209–227, 1994.
- B. Boufoussi, J. Casteren, and N. Mrhardy, “Generalized backward doubly stochastic differential equations and SPDEs with nonlinear Neumann boundary conditions,” Bernoulli, vol. 13, no. 2, pp. 423–446, 2007.
- N. El Karoui, C. Kapoudjian, E. Pardoux, S. Peng, and M. C. Quenez, “Reflected solutions of backward SDE's, and related obstacle problems for PDE's,” The Annals of Probability, vol. 25, no. 2, pp. 702–737, 1997.
- Y. Ren and L. Hu, “Reflected backward stochastic differential equations driven by Lévy processes,” Statistics & Probability Letters, vol. 77, no. 15, pp. 1559–1566, 2007.
- Y. Ren and M. El Otmani, “Generalized reflected BSDEs driven by a Lévy process and an obstacle problem for PDIEs with a nonlinear Neumann boundary condition,” Journal of Computational and Applied Mathematics, vol. 233, no. 8, pp. 2027–2043, 2010.
- Y. Ren, A. Lin, and L. Hu, “Stochastic PDIEs and backward doubly stochastic differential equations driven by Lévy processes,” Journal of Computational and Applied Mathematics, vol. 223, no. 2, pp. 901–907, 2009.
- S. Hamadène, “Reflected BSDE's with discontinuous barrier and application,” Stochastics and Stochastics Reports, vol. 74, no. 3-4, pp. 571–596, 2002.