Stochastic port--Hamiltonian systems

In the present work we formally extend the theory of port--Hamiltonian systems to include random perturbations. In particular, suitably choosing the space of flows and effort variables we will show how several elements coming from possibly different physical domains can be interconnected in order to describe a dynamics perturbed by general semimartingale. In this sense the noise does not enter the system solely as an external random perturbation but each port is a semimartingale in itself. We will show how the present treatment, extend pseudo-Poisson an pre--symplectic geometric mechanics. At last, we will show that a power preserving interconnection of stochastic port--Hamiltonian system defines again a stochastic port--Hamiltonian system