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Abstrakty
Generalized reflected backward stochastic differential equations have been considered so far only in the case of a deterministic interval. In this paper the existence and uniqueness of solution for generalized reflected backward stochastic differential equations in a convex domain with random terminal time is studied. Applications to the obstacle problem with Neumann boundary conditions for partial differential equations of elliptic type are given.
Słowa kluczowe
Wydawca
Rocznik
Tom
Strony
85--100
Opis fizyczny
Bibliogr. 11 poz.
Twórcy
autor
- Institute of Mathematics and Physics, University of Technology and Life Sciences, Kaliskiego 7, kaja@utp.edu.pl
Bibliografia
- [CIL] M.-G. Crandall, H. Ishii and P.-L. Lions, User’s guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc. 27 (1992), 1-67.
- [GP] A. Gégout-Petit et É. Pardoux, Équations différentielles stochastiques rétrogrades réflechiés dans un convexe, Stoch. Stoch. Rep. 57 (1996), 111-128.
- [J1] K. Jańczak, Discrete approximations of reflected backward stochastic differential equations with random terminal time, Probab. Math. Statist. 28 (2008), 41-74.
- [J2] K. Jańczak, Generalized reflected backward stochastic differential equations, Stochastics 81 (2009), 147-170.
- [LS] P.-L. Lions and A.-S. Sznitman, Stochastic differential equations with reflecting boundary conditions, Comm. Pure Appl. Math. 37 (1984), 511-537.
- [M] J.-L. Menaldi, Stochastic variational inequality for reflected diffusion, Indiana Univ. Math. J. 32 (1983), 733-744.
- [P] É. Pardoux, Backward stochastic differential equations and viscosity solutions of systems of semilinear parabolic and elliptic PDEs of second order, Stochastic Analysis and Related Topics, VI (Geilo, 1996), Progr. Probab. 42, Birkhäuser, 1998, 79-127.
- [PP] É. Pardoux and S. Peng, Adapted solutions of a backward stochastic differential equation, Systems Control Lett. 14 (1990), 55-61.
- [PR] É. Pardoux and A. Răşcanu, Backward stochastic differential equations with subdifferential operator and related variational inequalities, Stoch. Process. Appl. 76 (1998), 191-215.
- [PZ] É. Pardoux and S. Zhang, Generalized BSDEs and nonlinear Neumann boundary value problems, Probab. Theory Related Fields 110 (1998), 535-558.
- [RX] Y. Ren and N. Xia, Generalized reflected BSDE and an obstacle problem for PDEs with a nonlinear Neumann boundary condition, Stoch. Anal. Appl. 24 (2006), 1013-1033.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0065-0039