Abstract
We consider the following infinite dimensional backward stochastic evolution equation:
{-dY(t)=(A(t) Y(t) + f (t, Y(t), Z(t))) dt - Z(t) dW(t), Y(T)=xi,
where A(t), t >= 0, are unbounded operators that generate a strong evolution operator U(t, r), 0 <= r <= t <= T. We prove under non-Lipschitz conditions that such an equation admits a unique evolution solution. Some examples and regularity properties of this solution are given as well.