Journal of Theoretical Probability

, Volume 28, Issue 3, pp 1125–1144 | Cite as

On Two Multistable Extensions of Stable Lévy Motion and Their Semi-martingale Representations

  • Ronan Le Guével
  • Jacques Lévy Véhel
  • Lining Liu


We study two versions of multistable Lévy motion. Such processes are extensions of classical Lévy motion where the stability index is allowed to vary in time, a useful property for modeling non-increment stationary phenomena. We show that the two multistable Lévy 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 semi-martingales and provide semi-martingale decompositions.


Lévy motion Multistable process Semi-martingale 

Mathematics Subject Classification (2010)

60G44 60G51 60G52 



Support from SMABTP is gratefully acknowledged.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Ronan Le Guével
    • 1
  • Jacques Lévy Véhel
    • 2
  • Lining Liu
    • 2
  1. 1.Equipe de Statistique IrmarUniversité de Rennes 2-Haute BretagneRennes CedexFrance
  2. 2.Regularity Team, Inria & MAS LaboratoryEcole Centrale ParisChâtenay-Malabry CedexFrance

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