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Existence, uniqueness and stability of backward stochastic differential equations with locally monotone coefficient. (English. Abridged French version) Zbl 1017.60068

Summary: The authors prove existence, uniqueness and stability of the solution for multidimensional backward stochastic differential equations with locally monotone coefficient. This is done with an almost quadratic growth coefficient and a square integrable terminal data. The coefficient could be neither locally Lipschitz in the variable \(y\) nor in the variable \(z\).

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
35R60 PDEs with randomness, stochastic partial differential equations
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