Modeling and simulation of discontinuous dynamic recrystallization (DDRX) are now commonly carried out by numerical methods, most often finite element computation. It is also possible to use simple analytical approaches on the grain scale to get relevant information about the basic mechanisms involved in DDRX, in particular regarding the large strain steady state behaviour. This is illustrated in the present paper on the basis of a model previously proposed by the author and co-workers, which is first briefly presented. The macroscopic constitutive parameters associated with DDRX are then derived and three distinct "Derby exponents" are introduced for describing the relationship between steady state grain size and flow stress. Finally, it is shown, with the example of grain sizes, that not only can average quantities be predicted analytically, but also their distributions.