Multidimensional BSDE with Poisson jumps of Osgood type. (English) Zbl 1524.60134
Summary: This paper is devoted to solve a multidimensional backward stochastic differential equation with jumps in finite time horizon. Under linear growth generator, we prove existence and uniqueness of solution.
MSC:
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 60H05 | Stochastic integrals |
References:
| [1] | Barles, G., Buckdahn, R., Pardoux, É., Backward stochastic differential equations and integral-partial differential equations, Stochastics and Stochastics Reports60, (1996), 57-83. · Zbl 0878.60036 |
| [2] | Fan, S., Jiang, L., Davison, M., Existence and uniqueness for multidimensional BSDEs with generators of Osgood type, Frontiers of Mathematics in China8, (2013), 811-824. · Zbl 1306.60073 |
| [3] | Mao, X., Adapted solution of Backward stochastic differential equations with non-Lipschitz coefficients, Stochastic Processes and their Applications58, (1997), 281-292. · Zbl 0835.60049 |
| [4] | Pardoux, É., Peng, S., Adapted solutions of backward stochastic differential equations, Systems and Control Letters14, (1997), 55-61. · Zbl 0692.93064 |
| [5] | Pardoux, É., Peng, S. Backward doubly stochastic differential equations and semilinear PDEs. Probability Theory and Related Fields98, (1994), 209-227. · Zbl 0792.60050 |
| [6] | Pardoux, É., Peng, S., Backward stochastic differential equations and quasilinear parabolic PDEs, In: Rozosvskii, B.L., Sowers, R.S. (Eds). Stochastic partial differential equations and their applications, Lect. Notes in Control & Info. sci., Springer, Berlin, Heidelberg, New York176, (1992), 200-217. · Zbl 0766.60079 |
| [7] | Royer, M., Backward stochastic differential equations with jumps and related non-linear expectations, Stochastic Processes and their Applications116, (2006), 1358-1376. · Zbl 1110.60062 |
| [8] | Tang, S., Li, X., Necessary conditions for optimal control of stochastic systems with random jumps, SIAM J. Control Optim. 32, (5), (1994), 1447-1475. · Zbl 0922.49021 |
| [9] | Faye, I., Sow, A.B.: Finite and infinite time interval of BDSDES driven by L’EVY processes. African Diaspora Journal of Mathematics13, 108-126 (2012) · Zbl 1401.60104 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
