Nonlinear Feynman-Kac formula and discrete-functional-type BSDEs with continuous coefficients

Stochastic Processes and their Applications

Volumn 112, Issue 1, 2004, Pages 23-51

  Hu, Ying ^a   Ma, Jin ^b  

^a UNIVERSITÉ DE RENNES 1   (France)

^b PURDUE UNIVERSITY   (United States)

Author keywords

Backward SDEs with continuous coefficients; Discrete functionals; Measurable selections; Nonlinear Feynman Kac formulae

Indexed keywords

EID: 2542501546     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spa.2004.02.002     Document Type: Article

References (20)

1. Aronson D.G. Bounds for the fundamental solution of a parabolic equation Bull. Amer. Math. Soc. 73 1967 890-896
2. Aronson D.G. Non-negative solutions of linear parabolic equations Ann. Scuola Norm. Sup. Pisa 22 1968 607-694
3. Bertsekas D.P. Shreve S.E. Stochastic Optimal Control. The Discrete Time Case 1978 Academic Press New York
4. Bismut, J.M., 1976. Théorie Probabiliste du Contrôle des Diffusions. Mem. Amer. Math. Soc., Vol. 4 (167). Amer. Math. Soc., Providence, RI.
5. Çinlar E. Jacod J. Protter P. Sharpe M.J. Semimartingales and Markov processes Z. Wahrsch. Verw. Gebiete 54 2 1980 161-219
6. Dellacherie C. Meyer P.A. Probabilities and Potential 1978 North-Holland Publishing Co. Amsterdam
7. El Karoui, N., Mazliak, L. (Eds.), 1997. Backward Stochastic Differential Equations. Pitman Research Notes in Mathematics Series, Vol. 364, Longman, Harlow.
8. El Karoui N. Peng S. Quenez M.C. Backward Stochastic Differential Equations in finance Math. Finance 7 1 1997 1-71
9. Hamadene S. Équations différentielles stochastiques rétrogrades: les cas localement Lipschitzien Ann. Inst. H. Poincaré Probab. Statist. 32 5 1996 645-659
10. Hamadene S. Lepeltier J.P. Peng S. BSDEs with continuous coefficients and stochastic differential games El Karoui N. Mazliak L. Backward Stochastic Differential Equations (Paris, 1995-1996) Pitman Research Notes in Mathematics Series Vol. 364 1997 115-128 Longman Harlow
11. Kobylanski M. Backward stochastic differential equations and partial differential equations with quadratic growth Ann. Probab. 28 2 2000 558-602
12. Ladyzenskaja O.A. Solonnikov V.A. Ural'ceva N.N. Linear and Quasilinear Equations of Parabolic Type 1968 American Mathematical Society Providence, RI
13. Lepeltier J.P. San Martin J. Backward stochastic differential equations with continuous coefficient Statist. Probab. Lett. 32 4 1997 425-430
14. Lepeltier J.P. San Martin J. Existence for BSDE with superlinear-quadratic coefficient Stochastics Stochastics Rep. 63 3-4 1998 227-240
15. Ma, J., Yong, J., 1999. Forward-backward Stochastic Differential Equations and Their Applications. Lecture Notes in Mathematics, Vol. 1702. Springer, Berlin.
16. Ma J. Zhang J. Representation theorems for backward stochastic differential equations Ann. Appl. Probab. 12 4 2002 1390-1418
17. Ma J. Protter P. Yong J. Solving forward-backward stochastic differential equations explicitly-a four step scheme Probab. Theory Relat. Fields 98 3 1994 339-359
18. Pardoux E. Peng S. Adapted solution of a backward stochastic differential equation Systems Control Lett. 14 1 1990 55-61
19. Pardoux, E., Peng, S., 1992. Backward Stochastic Differential Equations and Quasilinear Parabolic Partial Differential Equations. Stochastic Partial Differential Equations and Their Applications (Charlotte, NC, 1991). Lecture Notes in Control and Information Science, Vol. 176. Springer, Berlin, pp. 200-217.
20. Zhang Y. Zheng W. Discretizing a backward stochastic differential equation Internat. J. Math. Math. Sci. 32 2 2002 103-116