Abstract
Let Y = (Y (t)) t ≥ 0 be a Lévy process on the real line and T be a Gamma random variable independent from Y. We proved that, for all p > 1, Y (T) and Y (T)∕T p are independent if, and only if, Y is stable with parameter 1∕p. This represents an extension of the result given by Letac and Seshadri [4] which represents the case where T is an exponential random variable.
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Louati, M., Masmoudi, A., Mselmi, F. (2015). Gamma stopping and drifted stable processes. In: Jeribi, A., Hammami, M., Masmoudi, A. (eds) Applied Mathematics in Tunisia. Springer Proceedings in Mathematics & Statistics, vol 131. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-18041-0_13
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DOI: https://doi.org/10.1007/978-3-319-18041-0_13
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-18040-3
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