On solutions of backward stochastic differential equations with jumps and applications

Stochastic Processes and their Applications

Volumn 66, Issue 2, 1997, Pages 209-236

  Situ, Rong ^a  

^a SUN YAT SEN UNIVERSITY   (China)

Author keywords

Adapted solution; BSDE with jumps; Convergence theorem; Ito formula; PDIE

Indexed keywords

EID: 0031588876     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0304-4149(96)00120-2     Document Type: Article

References (17)

1. A. Bensoussan, Lectures on stochastic control, in: S.K. Mittler and A. Moro, eds., Nonlinear Filtering and Stochastic Control, Lecture Notes in Mathematics, Vol. 972. (Springer, Berlin 1982) pp. 1-62.
2. J.M. Bismut, Theorie probabiliste du controle des diffusions, Mem Amer Math. Soc. 176 (1973) 1-30.
3. N.V. Krylov, Controlled Diffusion Proceses (Springer, Berlin, 1980).
4. O.A. Ladyzenskaja, V.A. Solonnikov and N.N. Uralceva, Linear and Quasi-linear Equations of Parabolic Type, Translations of Monographs 23 (AMS, Providence, RI, 1968).
5. X. Mao, Adapted solutions of backward stochastic differential equations with non-Lipschitz coefficients, Stochastic Process. Appl. 58 (1995) 281-292.
6. S. Marhno, The first boundary problem for integral-differential equations, Theory of Stochastic Processes 4 (1976) Kiev, 66-72 (in Russian).
7. E. Pardoux and S. Peng, Adapted solution of a backward stochastic differential equation, Systems & Control Lett. 14 (1990) 55-61.
8. E. Pardoux and S. Peng, Backward doubly stochastic differential equations and systems of quasilinear stochastic partial differential equations, Probab. Theory Related Fields 98 (1994) 2
9. S. Peng, A general stochastic maximum principle for optimal control problems, SIAM J. Control Optim. 28 (1990) 966-979.
10. S. Peng, Probabilistic interpletation for systems of quasilinear parabolic partial differential equations, Stochastics and Stochastics Reports 32 (1991) 61-74.
11. S. Peng, A generalized dynamic programming principle and Hamilton-Jacobi-Bellman equation, Stochastics and Stochastics Reports 38 (1992) 119-134.
12. S. Peng, Backward stochastic differential equations and applications to optimal control, Appl. Math. Optim. 27 (1993) 125-144.
13. R. Situ, On strong solution, uniqueness, stability and comparison theorem for a stochastic system with Poisson jumps, Lecture Notes in Control & Inform. Sci; vol. 75, Distributed Parameter System (Springer, Berlin, 1985) 352-381.
14. R. Situ, Theory and application of stochastic differential equations in China, Contemporary Math. 118 (Amer. Math. Soci., Providence, RI, 1991) 263-280.
15. R, Situ, A maximum principle for optimal controls of stochastic systems with random jumps, Proc. National Conf. on Control Theory and its Applications, Qingdao (1991) 1-7.
16. R. Situ and W.L. Chen, Existence of solutions and optimal control for reflecting stochastic differential equations with applications to population control theory, Stochastic Anal. Appl. 10 (1992) 45-106.
17. S. Tang and X. Li, Necessary conditions for optimal control of stochastic systems with random jumps, SIAM J. Control Optim. 32 (1994) 1447-1475.