**2. Microscopic and mesoscopic processes in deterministic dynamics**

#### **2.1 Microscopic dynamics: Definitions and notations**

It has been shown recently [18] that coarse-grained Hamiltonian systems can be approximated by Markov processes provided that they satisfy reasonable

*Stochastic Theory of Coarse-Grained Deterministic Systems: Martingales and Markov… DOI: http://dx.doi.org/10.5772/intechopen.95903*

properties, covering many realistic cases. These conclusions can be extended to a large class of deterministic systems generalizing classical Hamiltonian systems, which we now describe. We first specify our hypotheses and notations.
