Backward stochastic differential equations with locally monotone coefficient, preprint

We prove an existence and uniqueness result for backward stochastic differential equa-tions whose coefficients satisfy a stochastic monotonicity condition. In this setting, we deal with both constant and random terminal times. In the random case, the terminal time is allowed to take infinite values. But in aMarkovian framework, that is coupled with a forward SDE, our result provides a probabilistic interpretation of solutions to nonlinear PDEs. 1