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Time since maximum of Brownian motion and asymmetric Lévy processes

Martin, R and Kearney, Michael (2018) Time since maximum of Brownian motion and asymmetric Lévy processes Journal of Physics A: Mathematical and Theoretical, 51 (27), 275001.

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Motivated by recent studies of record statistics in relation to strongly correlated time series, we consider explicitly the drawdown time of a Lévy process, which is defined as the time since it last achieved its running maximum when observed over a fixed time period . We show that the density function of this drawdown time, in the case of a completely asymmetric jump process, may be factored as a function of t multiplied by a function of T  −  t. This extends a known result for the case of pure Brownian motion. We state the factors explicitly for the cases of exponential down-jumps with drift, and for the downward inverse Gaussian Lévy process with drift.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Electronic Engineering
Authors :
Martin, R
Date : 7 June 2018
DOI : 10.1088/1751-8121/aac191
Copyright Disclaimer : This is an author-created, un-copyedited version of an article published in Journal of Physics A: Mathematical and Theoretical. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at 10.1088/1751-8121/aac191
Depositing User : Melanie Hughes
Date Deposited : 12 Jun 2018 15:59
Last Modified : 07 Jun 2019 02:08

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