Exact Controllability Of Linear Stochastic Differential Equations And Related Problems

A notion of Lp-exact controllability is introduced for linear controlled (forward) stochastic differential equations with random coefficients. Several sufficient conditions are established for such kind of exact controllability. Further, it is proved that the Lp-exact controllability, the validity of an observability inequality for the adjoint equation, the solvability of an optimization problem, and the solvability of an Lp-type norm optimal control problem are all equivalent