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2012 | 32 | 1-2 | 69-85
Tytuł artykułu

Discrete approximations of generalized RBSDE with random terminal time

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Języki publikacji
EN
Abstrakty
EN
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.
Twórcy
  • Institute of Mathematics and Physics, University of Technology and Life Sciences, Kaliskiego 7, 85-796 Bydgoszcz, Poland
Bibliografia
  • [1] V. Bally, Approximation scheme for solutions of BSDE, Pitman Res. Notes Math. Ser. 364 Longman Harlow (1997) 177-191.
  • [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.
  • [3] P. Briand, B. Delyon and J. Mémin, Donsker-Type theorem for BSDEs, Elect. Comm. in Probab. 6 (2001) 1-14.
  • [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.
  • [5] A. Gegout-Petit and É. Pardoux, Equations diffréntielles stochastiques rétrogrades réfléchies dans un convexe, Stoch. Stoch. Rep. 57 (1996) 111-128.
  • [6] K. Jańczak, Discrete approximations of reflected backward stochastic differential equations with random terminal time, Probab. Math. Statistics 28 (2008) 41-74.
  • [7] K. Jańczak, Generalized reflected backward stochastic differential equations, Stochastics 81 (2009) 147-170. doi: 10.1080/17442500802299007.
  • [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] P.L. Lions and A.S. Sznitman, Stochastic differential equations with reflecting boundary conditions, Comm. Pure Appl. Math. (1984) 511-537.
  • [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.
  • [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.
  • [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.
  • [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.
  • [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.
  • [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.
  • [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.
  • [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.
  • [18] S. Toldo, Stability of solutions of BSDEs with random terminal time, SAIM Probab. Stat. 10 (2006) 141-163. doi: 10.1051/ps:2006006.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1145
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