Large deviations for power-law thinned Lévy processes

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This paper deals with the large deviations behavior of a stochastic process called a thinned Lévy process. This process appeared recently as a stochastic-process limit in the context of critical inhomogeneous random graphs (Bhamidi et al. (2012)). 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 Lévy process. General principles prescribe that the tilt should follow from a variational problem, but in the case of the thinned Lévy 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.

Originele taal-2Engels
Pagina's (van-tot)1353-1384
Aantal pagina's32
TijdschriftStochastic Processes and their Applications
Volume126
Nummer van het tijdschrift5
DOI's
StatusGepubliceerd - 1 mei 2016

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