  Stochastic infinite-dimensional port-Hamiltonian systems (SPHSs) with
multiplicative Gaussian white noise are considered. In this article we extend
the notion of Dirac structure for deterministic distributed parameter
port-Hamiltonian systems to a stochastic ones by adding some additional
stochastic ports. Using the Stratonovich formalism of the stochastic integral,
the proposed extended interconnection of ports for SPHSs is proved to still
form a Dirac structure. This constitutes our main contribution. We then deduce
that the interconnection between (stochastic) Dirac structures is again a
(stochastic) Dirac structure under some assumptions. These interconnection
results are applied on a system composed of a stochastic vibrating string
actuated at the boundary by a mass-spring system with external input and
output. This work is motivated by the problem of boundary control of SPHSs and
will serve as a foundation to the development of stabilizing methods.
