Abstract
The Lamperti correspondence gives a prominent role to two random time changes: the exponential functional of a Lévy process drifting to \(\infty\) and its inverse, the clock of the corresponding positive self-similar process. We describe here asymptotical properties of these clocks in large time, extending the results of Yor and Zani (Bernoulli 7, 351–362, 2001).
In memoriam, Marc Yor
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Acknowledgements
The authors want to thank Frédérique Petit for valuable conversations on the Cauchy clock.
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Demni, N., Rouault, A., Zani, M. (2015). Large Deviations for Clocks of Self-similar Processes. In: Donati-Martin, C., Lejay, A., Rouault, A. (eds) In Memoriam Marc Yor - Séminaire de Probabilités XLVII. Lecture Notes in Mathematics(), vol 2137. Springer, Cham. https://doi.org/10.1007/978-3-319-18585-9_19
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DOI: https://doi.org/10.1007/978-3-319-18585-9_19
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