Well Posedness of Operator Valued Backward Stochastic Riccati Equations   in Infinite Dimensional Spaces
  We prove existence and uniqueness of the mild solution of an infinite dimensional, operator valued, backward stochastic Riccati equation. We exploit the regularizing properties of the semigroup generated by the unbounded operator involved in the equation. Then the results will be applied to characterize the value function and optimal feedback law for a infinite dimensional, linear quadratic control problem with stochastic coefficients. 
Giuseppina Guatteri and Gianmario Tessitore
math.OC