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UID:www.tcs.tifr.res.in/event/851
DTSTAMP:20230914T125940Z
SUMMARY:Overdispersion and Multi-timescale Models: Exact Asymptotics
DESCRIPTION:Speaker: Michel Mandjes (University of Amsterdam \nKorteweg-de 
 Vries Institute for \nMathematics \nScience Park 904 \n1098 XH Amsterdam \
 nThe Netherlands)\n\nAbstract: \nPoisson processes are frequently used\, e
 .g. to model the customer arrival process in service systems\, or the clai
 m arrival proces in insurance models. In various situations\, however\, th
 e fluctuations in the arrival rate are so severe that the Poisson assumpti
 on ceases to hold. In a commonly followed approach to remedy this\, the de
 terministic parameter λ is replaced by a stochastic process Λ(t)\; in th
 is way the arrival process becomes “overdispersed”. The first part of 
 this talk considers the case that the Poisson rate is sampled periodically
 \, with a focus on an infinite-server queue fed by the resulting overdispe
 rsed arrival process. After having presented a functional central limit th
 eorem\, we concentrate on tail probabilities under a particular scaling of
  the arrival process and the sampling frequency. We derive logarithmic tai
 l asymptotics\, and in specific cases even exact tail asymptotics.\n\nIn t
 he second part of the talk we embed our overdispersion setting in a more g
 eneral framework. The probability of interest is expressed in terms of the
  composition of two Lévy processes\, which can alternatively be seen as a
  Lévy process with random time change. For this two-timescale model we pr
 esent exact tail asymptotics. The proof relies on an adaptation of classic
 al techniques developed by Bahadur and Rao\, in combination with delicate 
 Edgeworth expansion arguments. The resulting asymptotics have a remarkable
  form\, with finitely many sublinear terms in the exponent (joint work wit
 h Mariska Heemskerk and Julia Kuhn).\n
URL:https://www.tcs.tifr.res.in/web/events/851
DTSTART;TZID=Asia/Kolkata:20180123T143000
DTEND;TZID=Asia/Kolkata:20180123T153000
LOCATION:A-201 (STCS Seminar Room)
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