Large deviations for power-law thinned Levy processes
Abstract
This paper deals with the large deviations behavior of a stochastic process called thinned Levy process. This process appeared recently as a stochastic-process limit in the context of critical inhomogeneous random graphs. The process has a strong negative drift, while we are interested in the rare event of the process being positive at large times. To characterize this rare event, we identify a tilted measure. This presents some challenges inherent to the power-law nature of the thinned Levy process. General principles prescribe that the tilt should follow from a variational problem, but in the case of the thinned Levy process this involves a Riemann sum that is hard to control. We choose to approximate the Riemann sum by its limiting integral, derive the first-order correction term, and prove that the tilt that follows from the corresponding approximate variational problem is sufficient to establish the large deviations results.
Cite
@article{arxiv.1404.1692,
title = {Large deviations for power-law thinned Levy processes},
author = {Elie Aidekon and Remco van der Hofstad and Sandra Kliem and Johan S. H. van Leeuwaarden},
journal= {arXiv preprint arXiv:1404.1692},
year = {2014}
}