  Stochastic port-Hamiltonian systems on infinite-dimensional spaces governed
by It\^o stochastic differential equations (SDEs) are introduced and some
properties of this new class of systems are studied. They are an extension of
stochastic port-Hamiltonian systems defined on a finite-dimensional state
space. The concept of well-posedness in the sense of Weiss and Salamon is
generalized to the stochastic context. Under this extended definition,
stochastic port-Hamiltonian systems are shown to be well-posed. The theory is
illustrated on an example of a vibrating string subject to a Hilbert
space-valued Gaussian white noise process.
