Adapted solutions of backward stochastic differential equations with non- Lipschitz coefficients (Q1899270)

The author considers the following backward stochastic differential equation \[ x(t) = \int^1_tf \bigl( s,x(s), y(s) \bigr) ds + \int^1_t \biggl[ g \bigl( s,x (s) \bigr) + y( s) \biggr] dw(s) = X \tag{*} \] on \(0 \leq t \leq 1\). Here \(w(t)\) in a \(q\)-dimensional Brownian motion and \(y(t)\) is an adapted control process. He gives a theorem on the existence and uniqueness of the solution for (*) under a weaker condition than the Lipschitz one.