Journal Articles Journal of Theoretical Probability Year : 2015

On two multistable extensions of stable Lévy motion and their semimartingale representation

Abstract

We compare two definitions of multistable Lévy motions. Such processes are extensions of classical Lévy motion where the stability index is allowed to vary in time. 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 semimartingales and provide semimartingale decompositions.
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Dates and versions

hal-00730680 , version 1 (10-09-2012)
hal-00730680 , version 2 (24-10-2013)

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Ronan Le Guével, Jacques Lévy-Vehel, Lining Liu. On two multistable extensions of stable Lévy motion and their semimartingale representation. Journal of Theoretical Probability, 2015, 28 (3), pp.1125-1144. ⟨10.1007/s10959-013-0528-6⟩. ⟨hal-00730680v2⟩
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