  We consider a reaction-diffusion equation on a network subjected to dynamic
boundary conditions, with time delayed behaviour, also allowing for
multiplicative Gaussian noise perturbations. Exploiting semigroup theory, we
rewrite the aforementioned stochastic problem as an abstract stochastic partial
differential equation taking values in a suitable product Hilbert space, for
which we prove the existence and uniqueness of a mild solution. Eventually, a
stochastic optimal control application is studied.
