I propose to fully harness a new exciting window recently opened in Astrophysics, which I am pioneering: the study of multi-lambda fast variability from relativistic jets from stellar-mass compact objects. I will (a) identify and apply strategies to maximize the scientific output of a large amount of data, and formally define and publish new standard methods for multi-lambda statistical and timing analysis, to serve as points of reference for future works; (b) initiate an ambitious numerical code for the variable emission from a relativistic jet from a stellar-mass compact object; (c) apply the above techniques and codes to a large amount of data, placing unprecedented constraints to the physics of jets, and comparing the jet properties in black holes and neutron stars, ultimately answering the fundamental question about how the jet properties are influenced by the presence of a hard surface or an event horizon (and/or ergosphere), as well as by the presence of large-scale bipolar magnetic fields. I am one of the precursors in this field, which has already shown its large potential. I have built and am currently a leading member of a large international collaboration, which has acquired a large amount of data with the most diverse sets of observational facilities and data structure. The complexity of the field, together with its clear potential, demands a focussed and continuous effort, which I am planning to take. I will tackle the objective with a multi-disciplinary approach, working on observations, theory and numerical simulations, maximizing the scientific exploitation of the method. I have been hired recently by the host institution with a researcher permanent position, which guarantees my stability during the project and the feasibility of the project itself. As the topics of the proposed project nicely complement the present expertise at the host institution, the CIG funding will help me enourmously in integrating myself in the host institution.