### Uittreksel

Originele taal-2 | Engels |
---|---|

Plaats van productie | Eindhoven |

Uitgeverij | Eurandom |

Aantal pagina's | 27 |

Status | Gepubliceerd - 2014 |

### Publicatie series

Naam | Report Eurandom |
---|---|

Volume | 2014008 |

ISSN van geprinte versie | 1389-2355 |

### Vingerafdruk

### Citeer dit

*Large deviations for power-law thinned Lévy processes*. (Report Eurandom; Vol. 2014008). Eindhoven: Eurandom.

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*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.

Onderzoeksoutput: Boek/rapport › Rapport › Academic

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 -