It is stated that moving fluids can be described as fluctuating continua although their material distribution is always discontinuous. A stochastic particle transport is then considered by an imaginary ensemble of any number of equivalent turbulent fluids existing in parallel. This leads to exspectation values of the densities of turbulently transported particles. First a transport equation for a molecular self-diffusion is found. It is used as a reference for the difference between self-moving diffusing particles and transport through turbulent moving continua (e.g. aerosols). This is followed by a transport theory for longitudinal continuum fluctuations to provide an easier transition to the more complicated turbulent particle transport. The following transport equations arise: 1. -transport equation of molecular self-diffusion as partial differential equation as well as integral equation. The transition probabillity of velocities is calculated, explicitly. 2. -transport equation of a passive particle transport by longitudinal continuumfluktuations as partial differential equation as well as integral equation. The transition probabillity of velocities is calculated, explicitly. 3. -transport equation of a passive particle transport by turbulent continuum-fluktuations as partial differential equation as well as integral equation. The transition probabillity of velocities is calculated, explicitly. 2