Home | Contents | Submissions, editors, etc. | Login | Search | EJP
 Electronic Communications in Probability > Vol. 6 (2001) > Paper 1 open journal systems 


Donsker-Type Theorem for BSDEs

Philippe Briand, Université Rennes 1
Bernard Delyon, Université Rennes 1
Jean Mémin, Université Rennes 1


Abstract
This paper is devoted to the proof of Donsker's theorem for backward stochastic differential equations (BSDEs for short). The main objective is to give a simple method to discretize in time a BSDE. Our approach is based upon the notion of ``convergence of filtrations'' and covers the case of a (y,z)-dependent generator.


Full text: PDF

Pages: 1-14

Published on: January 10, 2001
Bibliography
  1. V. Bally, Approximation scheme for solutions of BSDE, Backward stochastic differential equations (N. El Karoui and L. Mazliak, eds.), Pitman Res. Notes Math. Ser., vol. 364, Longman, Harlow, 1997, pp. 177-191. Math. Review 2000k:60003 .
  2. D. Chevance, Numerical methods for backward stochastic differential equations, Numerical methods in finance, Cambridge Univ. Press, Cambridge, 1997, pp. 232-244. Math. Review 98i:60051 .
  3. D. Chevance, Résolution numériques des équations différentielles stochastiques rétrogrades , Ph.D. thesis, Université de Provence -- Aix-Marseille I, Marseille, 1997. Math. Review number not available.
  4. F. Coquet, V. Mackevicius, and J. Mémin, Corrigendum to: ``Stability in D of martingales and backward equations under discretization of filtration'' [Stochastic Processes Appl. 75 (1998)] , Stochastic Process. Appl. 82 (1999), no. 2, 335-338. Math. Review 2000e:60089 .
  5. F. Coquet, J. Mémin, and L. Slominski, On weak convergence of filtrations, Séminaire de Probabilités, XXXV, Lecture Notes in Math., Springer, Berlin, to appear.
  6. J. Douglas, J. Ma, and Ph. Protter, Numerical methods for forward-backward stochastic differential equations , Ann. Appl. Probab. 6 (1996), no. 3, 940-968. Math. Review 97k:60160 .
  7. N. El Karoui, S. Peng and M. C. Quenez, Backward stochastic differential equations in finance, Math. Finance 7 (1997), no. 1, 1--71. Math. Review 98d:90030 .
  8. J. Jacod, Convergence en loi de semimartingales et variation quadratique, Séminaire de Probabilités, XV, Lecture Notes in Math., vol. 850, Springer, Berlin, 1981, pp. 547-560. Math. Review 83c:60071 .
  9. J. Ma, Ph. Protter, and J. Yong, Solving forward-backward stochastic differential equations explicitly-a four step scheme , Probab. Theory Related Fields 98 (1994), no. 3, 339-359. Math. Review 94m:60118 .
  10. J. Ma and J. Yong, Forward-backward stochastic differential equations and their applications , Lecture Notes in Math., vol. 1702, Springer-Verlag, Berlin, 1999. Math. Review 2000k:60118 .
  11. J. Mémin and L. Slominski, Condition UT et stabilité en loi des solutions d'équations différentielles stochastiques , Séminaire de Probabilités, XXV, Lecture Notes in Math., vol. 1485, Springer, Berlin, 1991, pp. 162-177. Math. Review 93m:60121 .
  12. E. Pardoux and S.Peng, Adapted solution of a backward stochastic differential equations, Systems Control Lett. 14 (1990), no. 1, 55--61. Math. Review 91e:60171 .
  13. E. Pardoux and S.Peng, Backward stochastic differential equations and quasilinear parabolic partial differential equations , in Stochastic partial differential equations and their applications (Charlotte, NC, 1991), 200--217, Lecture Notes in Control and Inform. Sci., 176, Springer, Berlin, 1992. Math. Review 93k:60157 .
  14. S. Peng, Probabilistic interpretation for systems of quasilinear parabolic partial differential equations , Stochastics Stochastics Rep. 37 (1991), no. 1-2, 61--74. Math. Review 93a:35159 .
  15. L. Slominski, Stability of stochastic differential equations driven by general semimartingales , Dissertationes Math. (Rozprawy Mat.), vol. 349, Polish Academy of sciences, Warszawa, Poland, 1996. Math. Review 96m:60132 .
















Research
Support Tool
Capture Cite
View Metadata
Printer Friendly
Context
Author Address
Action
Email Author
Email Others


Home | Contents | Submissions, editors, etc. | Login | Search | EJP

Electronic Communications in Probability. ISSN: 1083-589X