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Splitting algorithm for nested events

By Ludovic Goudenège

Also appears in collection : CEMRACS - Summer school: Numerical methods for stochastic models: control, uncertainty quantification, mean-field / CEMRACS - École d'été : Méthodes numériques pour équations stochastiques : contrôle, incertitude, champ moyen

Consider a problem of Markovian trajectories of particles for which you are trying to estimate the probability of a event. Under the assumption that you can represent this event as the last event of a nested sequence of events, it is possible to design a splitting algorithm to estimate the probability of the last event in an efficient way. Moreover you can obtain a sequence of trajectories which realize this particular event, giving access to statistical representation of quantities conditionally to realize the event. In this talk I will present the "Adaptive Multilevel Splitting" algorithm and its application to various toy models. I will explain why it creates an unbiased estimator of a probability, and I will give results obtained from numerical simulations.

Information about the video

Citation data

  • DOI 10.24350/CIRM.V.19204103
  • Cite this video Goudenège, Ludovic (01/08/2017). Splitting algorithm for nested events. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19204103
  • URL https://dx.doi.org/10.24350/CIRM.V.19204103

Bibliography

  • Bréhier, C.-E., Gazeau, M., Goudenège, L., Lelièvre, T., & Rousset, M. (2016). Unbiasedness of some generalized adaptive multilevel splitting algorithms. The Annals of Applied Probability, 26(6), 3559-3601 - http://dx.doi.org/10.1214/16-AAP1185

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