Before revision:  In  [ 14 ] and [ 15 ] the authors showed  with the help of a multi-scale anal- ysis that stochastic systems with infinite and finite degrees of freedom can be approximated by dynamical systems whose leading order time evolution is given by a combination of ordi- nary differential equations and Markov chains.
After revision:  In the reverse sense attaching meaningful dynamics to given 'interaction diagrams' is a central bottleneck problem in many application areas, especially in cell biology where various such diagrams with different conventions describing molecular regulation are presently in use. In most situations these diagrams can only be interpreted by the use of both discrete and continuous variables during the modelling process, corresponding to both deterministic and stochastic hybrid dynamics. The conventions in genetics are well-known, and therefore we use this field for illustration purposes. In [ 14 ] and [ 15 ] the authors showed with the help of a multi-scale anal- ysis that stochastic systems with infinite and finite degrees of freedom can be approximated by dynamical systems whose leading order time evolution is given by a combination of ordi- nary differential equations and Markov chains.