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We discuss BSDE with drivers containing nonlinearities of the type p(y)|z| and p(y)|z| 2 with p a polynomial of any degree. Sucient conditions are given for existence and uniqueness of solutions as well as comparison results. We then connect the results to the Markovian FBSDE setting, discussing applications in the theory of PDE perturbation and stating a result concerning a large deviations principle for the rst component of the solution to the BSDE. 2010 AMS subject classications: Primary: 60H10; Secondary: 60J60, 60F10, 35B20.doi:10.1142/s0219493712500153 fatcat:uec75bsxq5ehjhm6sey5qeehzm