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

Ronan Le Guével (), Jacques Lévy Véhel () and Lining Liu ()
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Ronan Le Guével: Université de Rennes 2-Haute Bretagne
Jacques Lévy Véhel: Ecole Centrale Paris
Lining Liu: Ecole Centrale Paris

Journal of Theoretical Probability, 2015, vol. 28, issue 3, 1125-1144

Abstract: Abstract 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.

Keywords: Lévy motion; Multistable process; Semi-martingale; 60G44; 60G51; 60G52 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10959-013-0528-6

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