Optimal prediction for positive self-similar Markov processes

Erik J. Baurdoux, Andreas E. Kyprianou, Curdin Ott

Research output: Contribution to journalArticle

Abstract

This paper addresses the question of predicting when a positive self-similar Markov process X attains its pathwise global supremum or infimum before hitting zero for the first time (if it does at all). This problem has been studied in [9] under the assumption that X is a positive transient diffusion. We extend their result to the class of positive self-similar Markov processes by establishing a link to [3], where the same question is studied for a Lévy process drifting to −∞. The connection to [3] relies on the so-called Lamperti transformation [15] which links the class of positive self-similar Markov processes with that of Lévy processes. Our approach shows that the results in [9] for Bessel processes can also be seen as a consequence of self-similarity.
Original languageEnglish
Article number48
Number of pages24
JournalElectronic Journal of Probability
Volume21
DOIs
Publication statusPublished - 28 Jul 2016

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