Large deviations for power-law thinned Lévy processes

E.F. Aidekon, R.W. Hofstad, van der, S.M. Kliem, J.S.H. Leeuwaarden, van

Onderzoeksoutput: Boek/rapport › Rapport › Academic

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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

Vingerafdruk

Large Deviations
Power Law
Riemann sum
Rare Events
Tilt
Variational Problem
Stochastic Processes
Random Graphs
Limiting
Choose
Sufficient
First-order
Term

Citeer dit

Aidekon, E. F., Hofstad, van der, R. W., Kliem, S. M., & Leeuwaarden, van, J. S. H. (2014). Large deviations for power-law thinned Lévy processes. (Report Eurandom; Vol. 2014008). Eindhoven: Eurandom.
Aidekon, E.F. ; Hofstad, van der, R.W. ; Kliem, S.M. ; Leeuwaarden, van, J.S.H. / Large deviations for power-law thinned Lévy processes. Eindhoven : Eurandom, 2014. 27 blz. (Report Eurandom).
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Aidekon, EF, Hofstad, van der, RW, Kliem, SM & Leeuwaarden, van, JSH 2014, Large deviations for power-law thinned Lévy processes. Report Eurandom, vol. 2014008, Eurandom, Eindhoven.

Large deviations for power-law thinned Lévy processes. / Aidekon, E.F.; Hofstad, van der, R.W.; Kliem, S.M.; Leeuwaarden, van, J.S.H.

Eindhoven : Eurandom, 2014. 27 blz. (Report Eurandom; Vol. 2014008).

Onderzoeksoutput: Boek/rapport › Rapport › Academic

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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.

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Aidekon EF, Hofstad, van der RW, Kliem SM, Leeuwaarden, van JSH. Large deviations for power-law thinned Lévy processes. Eindhoven: Eurandom, 2014. 27 blz. (Report Eurandom).

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