Time-dependent multi-zone radiation transfer modeling of fast blazar variability

We present the first applications of a new time-dependent multi-zone jet radiation transfer code to the study the multiwavelength emission of the TeV Blazar Mrk 421. The code couples Fokker-Planck and Monte Carlo methods. For the first time all light travel time effects are fully considered as well as proper self-consistent treatment of Compton cooling, which depends on them. The first tests focus on the March 2001 observations of Mrk 421, still one of the best datasets available for phenomenology and X-ray/TeV data coverage. We summarize the results of scenarios of variability induced by injection of relativistic electrons in a blob encountering a shock, and with different combinations with a second component, either co-spatial or independent from the active region.