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Generalized RBSDEs with random terminal time and applications to PDEs

Jańczak-Borkowska K.

Bulletin of the Polish Academy of Sciences. Mathematics

2011

Vol. 59, no 1

85-100

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.

Discrete approximations of reflected backward stochastic differential equations with random terminal time

Jańczak K.

Probability and Mathematical Statistics

2008

Vol. 28, Fasc. 1

41--74

We study convergence of discrete approximations of reflected backward stochastic differential equations with random terminal time in a general convex domain. Applications to investigation of the viability property for backward stochastic differential equations and to obstacle problem for partial differential equations are given.