  In this paper, a stochastic Hamiltonian formulation (SHF) is proposed and
applied to dissipative particle dynamics (DPD) simulations. As an extension of
Hamiltonian dynamics to stochastic dissipative systems, the SHF provides
necessary foundations and great convenience for constructing efficient
numerical integrators. As a first attempt, we develop the St\"ormer--Verlet
type of schemes based on the SHF, which are structure-preserving for
deterministic Hamiltonian systems without external forces, the dissipative
forces in DPD. Long-time behaviour of the schemes is shown numerically by
studying the damped Kubo oscillator. In particular, the proposed schemes
include the conventional Groot-Warren's modified velocity-Verlet method and a
modified version of Gibson-Chen-Chynoweth as special cases. The schemes are
applied to DPD simulations and analysed numerically.
