Book of Abstracts WS MTM2011
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چکیده
Stimulated by the classical transposition method in PDEs, we introduced a new notion of solution, i.e., transposition solution to BSDEs/BSEEs. This is something like the generalized function solutions to PDEs. We obtained the well-posedness of linear and semilinear BSDEs/BSEEs in general filtration space, without using the Martingale Representation Theorem. As one application of our transposition method, we obtained a new numerical method for solving BSDEs. Our method can be viewed as an analogue of the classical finite element method solving deterministic PDEs. As another application of this transposition method, we established the Pontryagin-type maximum principle for optimal controls of general infinite dimensional nonlinear stochastic evolution equations, in which both drift and diffusion terms can contain the control variables, and the control domains are allowed to be nonconvex.
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تاریخ انتشار 2013