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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.
We establish existence and uniqueness for infinite dimensional Riccati equations taking values in the Banach space L 1 ($mu$ $otimes$ $mu$) for certain signed matrix measures $mu$ which are not necessarily finite. Such equations can be seen as the in
In this paper we study, by probabilistic techniques, the convergence of the value function for a two-scale, infinite-dimensional, stochastic controlled system as the ratio between the two evolution speeds diverges. The value function is represented a
There exist many ways to stabilize an infinite-dimensional linear autonomous control systems when it is possible. Anyway, finding an exponentially stabilizing feedback control that is as simple as possible may be a challenge. The Riccati theory provi
In this paper we are concerned with a new type of backward equations with anticipation which we call neutral backward stochastic functional differential equations. We obtain the existence and uniqueness and prove a comparison theorem. As an applicati
In this paper, we investigate the one-dimensional derivative nonlinear Schrodinger equations of the form $iu_t-u_{xx}+ilambdaabs{u}^k u_x=0$ with non-zero $lambdain Real$ and any real number $kgs 5$. We establish the local well-posedness of the Cauch