Discrete approximations of generalized RBSDE with random terminal time

Katarzyna Jańczak-Borkowska

Discussiones Mathematicae Probability and Statistics (2012)

  • Volume: 32, Issue: 1-2, page 69-85
  • ISSN: 1509-9423

Abstract

top
The convergence of discrete approximations of generalized reflected backward stochastic differential equations with random terminal time in a general convex domain is studied. Applications to investigation obstacle elliptic problem with Neumann boundary condition for partial differential equations are given.

How to cite

top

Katarzyna Jańczak-Borkowska. "Discrete approximations of generalized RBSDE with random terminal time." Discussiones Mathematicae Probability and Statistics 32.1-2 (2012): 69-85. <http://eudml.org/doc/271072>.

@article{KatarzynaJańczak2012,
abstract = {The convergence of discrete approximations of generalized reflected backward stochastic differential equations with random terminal time in a general convex domain is studied. Applications to investigation obstacle elliptic problem with Neumann boundary condition for partial differential equations are given.},
author = {Katarzyna Jańczak-Borkowska},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {generalized reflected BSDE; discrete approximation methods; viscosity solution; reflected backward stochastic differential equations; discrete approximations},
language = {eng},
number = {1-2},
pages = {69-85},
title = {Discrete approximations of generalized RBSDE with random terminal time},
url = {http://eudml.org/doc/271072},
volume = {32},
year = {2012},
}

TY - JOUR
AU - Katarzyna Jańczak-Borkowska
TI - Discrete approximations of generalized RBSDE with random terminal time
JO - Discussiones Mathematicae Probability and Statistics
PY - 2012
VL - 32
IS - 1-2
SP - 69
EP - 85
AB - The convergence of discrete approximations of generalized reflected backward stochastic differential equations with random terminal time in a general convex domain is studied. Applications to investigation obstacle elliptic problem with Neumann boundary condition for partial differential equations are given.
LA - eng
KW - generalized reflected BSDE; discrete approximation methods; viscosity solution; reflected backward stochastic differential equations; discrete approximations
UR - http://eudml.org/doc/271072
ER -

References

top
  1. [1] V. Bally, Approximation scheme for solutions of BSDE, Pitman Res. Notes Math. Ser. 364 Longman Harlow (1997) 177-191. Zbl0889.60068
  2. [2] V. Bally and G. Pages, Error analysis of the optimal quantization algorithm for obstacle problems, Stochastic Process. Appl. 106 (1) (2003) 1-40. doi: 10.1016/S0304-4149(03)00026-7. Zbl1075.60523
  3. [3] P. Briand, B. Delyon and J. Mémin, Donsker-Type theorem for BSDEs, Elect. Comm. in Probab. 6 (2001) 1-14. Zbl0977.60067
  4. [4] P. Briand, B. Delyon and J. Mémin, On the robustness of backward stochastic diffrential equations, Stochastic Process. Appl. 97 (2002) 229-253. doi: 10.1016/S0304-4149(01)00131-4. Zbl1058.60041
  5. [5] A. Gegout-Petit and É. Pardoux, Equations diffréntielles stochastiques rétrogrades réfléchies dans un convexe, Stoch. Stoch. Rep. 57 (1996) 111-128. Zbl0891.60050
  6. [6] K. Jańczak, Discrete approximations of reflected backward stochastic differential equations with random terminal time, Probab. Math. Statistics 28 (2008) 41-74. Zbl1147.60036
  7. [7] K. Jańczak, Generalized reflected backward stochastic differential equations, Stochastics 81 (2009) 147-170. doi: 10.1080/17442500802299007. Zbl1165.60327
  8. [8] K. Jańczak-Borkowska, Generalized RBSDE with random terminal time, Bull. Polish Acad. Sci. Math. 59 (2011) 85-100. doi: 10.4064/ba59-1-10. 
  9. [9] P.L. Lions and A.S. Sznitman, Stochastic differential equations with reflecting boundary conditions, Comm. Pure Appl. Math. (1984) 511-537. Zbl0598.60060
  10. [10] J. Ma, P. Protter, J. San Martin and S. Torres, Numerical method for backward stochastic differential equations, Ann. Appl. Probab. 12 (2002) 302-316. doi: 10.1214/aoap/1015961165. Zbl1017.60074
  11. [11] J. Ma and J. Zhang, Representation and regularities for solutions to BSDEs with reflections, Stochastic Process. Appl. 115 (2005) 539-569. doi: 10.1016/j.spa.2004.05.010. Zbl1076.60049
  12. [12] J.L. Menaldi, Stochastic variational inequality for reflected diffusion, Indiana Univ. Math. Journal 32 (1983) 733-744. doi: 10.1512/iumj.1983.32.32048. Zbl0492.60057
  13. [13] É. Pardoux and S. Peng, Adapted solutions of a backward stochastic differential equation, Systems Control Lett. 14 (1990) 55-61. doi: 10.1016/0167-6911(90)90082-6. Zbl0692.93064
  14. [14] É. Pardoux and A. Răşcanu, Backward stochastic differential equations with subdifferential operator and related variational inequalities, Stochastic Process. Appl. 76 (1998) 191-215. doi: 10.1016/S0304-4149(98)00030-1. Zbl0932.60070
  15. [15] É. Pardoux and S. Zhang, Generalized BSDEs and nonlinear Neumann boundary value problems, Probab. Theory Relat. Fields 110 (1998) 535-558. doi: 10.1007/s004400050158. Zbl0909.60046
  16. [16] Y. Ren and N. Xia, Generalized reflected BSDE and an obstacle problem for PDEs with a nonlinear Neumann boundary condition, Stochastic Analysis and Applications 24 (2006) 1-21. doi: 10.1080/07362990600870454. Zbl1122.60055
  17. [17] L. Słomiński, Euler's approximations of solutions of SDE's with reflecting boundary, Stochastic Process. Appl. 94 (2001) 317-337. doi: 10.1016/S0304-4149(01)00087-4. Zbl1053.60062
  18. [18] S. Toldo, Stability of solutions of BSDEs with random terminal time, SAIM Probab. Stat. 10 (2006) 141-163. doi: 10.1051/ps:2006006. Zbl1185.60064

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.