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Generalized RBSDEs with Random Terminal Time and Applications to PDEs

Katarzyna Jańczak-Borkowska (2011)

Bulletin of the Polish Academy of Sciences. Mathematics

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.

Generalized solutions to hybrid dynamical systems

Ricardo G. Sanfelice, Rafal Goebel, Andrew R. Teel (2008)

ESAIM: Control, Optimisation and Calculus of Variations

Several recent results in the area of robust asymptotic stability of hybrid systems show that the concept of a generalized solution to a hybrid system is suitable for the analysis and design of hybrid control systems. In this paper, we show that such generalized solutions are exactly the solutions that arise when measurement noise in the system is taken into account.

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