Optimal prediction for positive self-similar Markov processes

Baurdoux, Erik J., 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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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
Library of Congress subject classification:	Q Science > QA Mathematics
Project and Funder Information:	Project ID Funder Name Funder ID EP/L002442/1 Engineering and Physical Sciences Research Council http://dx.doi.org/10.13039/501100000266
Date Deposited:	21 Sep 2016 13:25
URL:	http://eprints.lse.ac.uk/67820/

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