Résumé
In the context of biology and ecology, stochastic differential equations (SDE) can be seen as an intermediate modeling tool between macroscopic dynamics, usually deterministic and continuous, and microscopic dynamics, usually discrete and random. Ordinary differential equations used as modeling tools for macroscopic dynamics are relatively well understood; their numerical simulation is also well developed. Pure jump Markov processes are usually used for modeling microscopic dynamics; they are also relatively well understood and can be efficiently simulated (at least in small population sizes). We also have a good comprehension of SDE’s as well as their simulation algorithms. However, hybridization of these different types of models and their interconnections in a rigorous framework in terms of analysis, as well as simulation, still remain an open question. We will introduce this problem and discuss a number of promising leads.