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BEGIN:VEVENT
UID:news250@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20180716T222212
DTSTART;TZID=Europe/Zurich:20150901T110000
SUMMARY:Seminar in Numerical Analysis: Abdul-Lateef Haji-Ali (King Abdullah
  University)
DESCRIPTION:I discuss using single level and multilevel Monte Carlo  method
 s to compute quantities of interests of a stochastic particle  system in t
 he mean-field. In this context\, the stochastic particles  follow a couple
 d system of Ito stochastic differential equations (SDEs).  Moreover\, this
  stochastic particle system converges to a stochastic  mean-field limit as
  the number of particles tends to infinity.\\r\\nIn  2012\, my Master thes
 is developed different versions of Multilevel Monte  Carlo (MLMC) for part
 icle systems\, both with respect to time steps and  number of particles an
 d proposed using particle antithetic estimators  for MLMC. In that thesis\
 , I showed moderate savings of MLMC compared to  Monte Carlo. In this talk
 \, I recall and expand on these results\,  emphasizing the importance of a
 ntithetic estimators in stochastic  particle systems. I will finally concl
 ude by proposing the use of our  recent Multi-index Monte Carlo method to 
 obtain improved convergence  rates.
X-ALT-DESC:I discuss using single level and multilevel Monte Carlo  methods
  to compute quantities of interests of a stochastic particle  system in th
 e mean-field. In this context\, the stochastic particles  follow a coupled
  system of Ito stochastic differential equations (SDEs).  Moreover\, this 
 stochastic particle system converges to a stochastic  mean-field limit as 
 the number of particles tends to infinity.\nIn  2012\, my Master thesis de
 veloped different versions of Multilevel Monte  Carlo (MLMC) for particle 
 systems\, both with respect to time steps and  number of particles and pro
 posed using particle antithetic estimators  for MLMC. In that thesis\, I s
 howed moderate savings of MLMC compared to  Monte Carlo. In this talk\, I 
 recall and expand on these results\,  emphasizing the importance of antith
 etic estimators in stochastic  particle systems. I will finally conclude b
 y proposing the use of our  recent Multi-index Monte Carlo method to obtai
 n improved convergence  rates. 
DTEND;TZID=Europe/Zurich:20150901T120000
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