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Optimal prediction for positive self-similar Markov processes

Baurdoux, Erik J. and Kyprianou, Andreas E. and Ott, Curdin (2016) Optimal prediction for positive self-similar Markov processes. Electronic Journal of Probability, 21. p. 48. ISSN 1083-6489

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Identification Number: 10.1214/16-EJP4280

Abstract

This paper addresses the question of predicting when a positive self-similar Markov process XX 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 XX 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.

Item Type: Article
Official URL: https://projecteuclid.org/info/euclid.ejp
Additional Information: © 2016 The Institute of Mathematical Statistics and the Bernoulli Society © CC BY 4.0
Subjects: Q Science > QA Mathematics
Date Deposited: 21 Sep 2016 13:25
Last Modified: 21 Sep 2016 14:00
Projects: EP/L002442/1
Funders: Engineering and Physical Sciences Research Council
URI: http://eprints.lse.ac.uk/id/eprint/67820

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