Time since maximum of Brownian motion and asymmetric Levy processes
Probability
2020-02-27 v1
Abstract
Motivated by recent studies of record statistics in relation to strongly correlated time series, we consider explicitly the drawdown time of a Levy process, which is defined as the time since it last achieved its running maximum when observed over a fixed time period [0,T]. 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 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 Levy process with drift.
Keywords
Cite
@article{arxiv.1811.00827,
title = {Time since maximum of Brownian motion and asymmetric Levy processes},
author = {Richard J. Martin and Michael J. Kearney},
journal= {arXiv preprint arXiv:1811.00827},
year = {2020}
}