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- W2056932936 abstract "We consider a second order semi-elliptic differential operator L with measurable coefficients, in divergence form, and the semilinear parabolic system of PDE’s $$(partial _{t}+L)u(t,x)+f(t,x,u,nabla usigma )=0,quad forall 0leqslant tleqslant T,$$ $$u(T,x)=Phi (x).$$ We solve this system in the framework of Dirichlet spaces and employ the symmetric Markov process of infinitesimal operator L in order to obtain a precised version of the solution u by solving the corresponding system of backward stochastic differential equations. This precised version verifies pointwise the so called “mild equation”, which is equivalent to the above PDE. As a technical ingrediend we prove a representation theorem for arbitrary martingales which generalises a result of Fukushima for martingale additive functionals. The nonlinear term f satisfies a monotonicity condition with respect to u and a Lipschitz condition with respect to ∇u." @default.
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- W2056932936 date "2005-02-01" @default.
- W2056932936 modified "2023-10-03" @default.
- W2056932936 title "Backward Stochastic Differential Equations Associated to a Symmetric Markov Process" @default.
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- W2056932936 doi "https://doi.org/10.1007/s11118-003-6457-8" @default.
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