On two multistable extensions of stable L\'evy motion and their   semimartingale representation
  We compare two definitions of multistable L\'evy motions. Such processes are extensions of classical L\'evy motion where the stability index is allowed to vary in time. We show that the two multistable L\'evy motions have distinct properties: in particular, one is a pure-jump Markov process, while the other one satisfies neither of these properties. We prove that both are semimartingales and provide semimartingale decompositions. 
Ronan Le Gu\'evel (IRMAR), Jacques L\'evy-Vehel (INRIA Saclay - Ile de   France, MAS), Lining Liu (INRIA Saclay - Ile de France)
math.PR