TY - BOOK
T1 - Large deviations for power-law thinned Lévy processes
AU - Aidekon, E.F.
AU - Hofstad, van der, R.W.
AU - Kliem, S.M.
AU - Leeuwaarden, van, J.S.H.
PY - 2014
Y1 - 2014
N2 - 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.
AB - 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.
M3 - Report
T3 - Report Eurandom
BT - Large deviations for power-law thinned Lévy processes
PB - Eurandom
CY - Eindhoven
ER -