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 thinned Lévy 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 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
Plaats van productieEindhoven
UitgeverijEurandom
Aantal pagina's27
StatusGepubliceerd - 2014

Publicatie series

NaamReport Eurandom
Volume2014008
ISSN van geprinte versie1389-2355

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