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SUMMARY:Importance Sampling for McKean-Vlasov Stochastic Differential Equa
 tion
DTSTART:20230922T141500
DTEND:20230922T154500
DTSTAMP:20260510T022858Z
UID:ba39d0c58c31de3f2974161e53d926c494a54269606538fb1075ae51
CATEGORIES:Conferences - Seminars
DESCRIPTION:Dr Nadhir Ben Rached - University of Leeds\, UK\n\nAbstract: 
 We are interested in Monte Carlo (MC) methods for estimating probabilities
  of rare events associated with solutions to the McKean-Vlasov stochasti
 c differential equation (MV-SDE). MV-SDEs arise in the mean-field limit of
  stochastic interacting particle systems\, which have many applications in
  pedestrian dynamics\, collective animal behaviour and financial mathemati
 cs. Importance sampling (IS) is used to reduce high relative variance in M
 C estimators of rare event probabilities. Optimal change of measure is met
 hodically derived from variance minimisation\, yielding a high-dimensional
  partial differential control equation which is cumbersome to solve. This 
 problem is circumvented by using a decoupling approach\, resulting in a lo
 wer dimensional control PDE. The decoupling approach necessitates the use 
 of a double Loop Monte Carlo (DLMC) estimator. We further combine IS with 
 a novel multilevel DLMC estimator which not only reduces complexity from O
 (TOL-4) to O(TOL-3) but also drastically reduces associated constant\,
  enabling computationally feasible estimation of rare event probabilities
 .\n\n \n\n\nJoint work with Shyam Mohan\, Abdul-Lateef Haji-Ali\, and Rau
 l Tempone.\n\n-------
LOCATION:CM 0 9 https://plan.epfl.ch/?room==CM%200%209
STATUS:CONFIRMED
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