SOLUTION AND CONTROL OF A BILINEAR STOCHASTIC DELAY EQUATION

A bilinear stochastic delay equation with delay in the coefficients of the noise is considered. When the equation is rewritten in abstract form in Hilbert spaces, the coefficients of the noise are unbounded operators. A direct solution of the abstract equation is presented, under a general assumption which allows unification of this class of delay equations with a class of parabolic equations. Finally, the linear quadratic regulator problem governed by this equation is studied by a direct solution of the associated Riccati equation.