  In this paper, we study infinite dimensional stochastic systems having both
unbounded control and observation operators. First of all, using a semigroup
approach, we give another take of the well-posedness of such systems treated in
[SIAM J. Control Optim., 53 (2015), pp. 3457--3482]. We further prove a result
on the exact controllability of such systems. Second, we propose a new
variation of constants formula for mild solutions of perturbed abstract
stochastic Cauchy problems using the concept of Yosida extensions of admissible
operators. Third, we prove the well-posedness of perturbed boundary control
systems. Fourth, we apply this result to a general class of stochastic systems
with delays in the state, control, and observation parts. Finally, we study
admissible observation operators and exact observability for semilinear
stochastic systems.
