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2016 Optimal prediction for positive self-similar Markov processes
Erik J. Baurdoux, Andreas E. Kyprianou, Curdin Ott
Electron. J. Probab. 21: 1-24 (2016). DOI: 10.1214/16-EJP4280


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 $-\infty $. 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.


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Erik J. Baurdoux. Andreas E. Kyprianou. Curdin Ott. "Optimal prediction for positive self-similar Markov processes." Electron. J. Probab. 21 1 - 24, 2016.


Received: 4 May 2015; Accepted: 11 April 2016; Published: 2016
First available in Project Euclid: 28 July 2016

zbMATH: 1346.60121
MathSciNet: MR3539642
Digital Object Identifier: 10.1214/16-EJP4280

Primary: 60G40
Secondary: 60G51, 60J75


Vol.21 • 2016
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