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.
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Le Guével, R., Lévy Véhel, J. & Liu, L. On Two Multistable Extensions of Stable Lévy Motion and Their Semi-martingale Representations. J Theor Probab 28, 1125–1144 (2015). https://doi.org/10.1007/s10959-013-0528-6
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DOI: https://doi.org/10.1007/s10959-013-0528-6