  Multi-agent systems can be successfully described by kinetic models, which
allow one to explore the large scale aggregate trends resulting from elementary
microscopic interactions. The latter may be formalised as collision-like rules,
in the spirit of the classical kinetic approach in gas dynamics, but also as
Markov jump processes, which assume that every agent is stimulated by the other
agents to change state according to a certain transition probability
distribution. In this paper we establish a parallelism between these two
descriptions, whereby we show how the understanding of the kinetic jump process
models may be improved taking advantage of techniques typical of the
collisional approach.
