A branching L\'evy process can be seen as the continuous-time version of a branching random walk. It describes a particle system on the real line in which particles move and reproduce independently one of the others, in a Poissonian manner. Just as for L\'evy processes, the law of a branching L\'evy process is determined by its characteristic triplet $(\sigma^2,a,\Lambda)$, where the L\'evy measure $\Lambda$ describes the intensity of the Poisson point process of births and jumps. We establish a version of Biggins' theorem on martingale convergence for branching random walks in this framework. That is we provide necessary and sufficient conditions in terms of the characteristic triplet $(\sigma^2,a,\Lambda)$ for additive martingales of branching L\'evy processes to have a non-degenerate limit. The proof is adapted from the spinal decomposition argument of Lyons. 查看全文>>