Multilevel Splitting

  • Amarjit BudhirajaEmail author
  • Paul Dupuis
Part of the Probability Theory and Stochastic Modelling book series (PTSM, volume 94)


An alternative to importance sampling in estimating rare events and related functionals is multilevel splitting. In the context of estimating probabilities of a set \(\mathscr {C}\) in path space, the multilevel splitting philosophy is to simulate particles that evolve according to the law of \(\left\{ X_{i}\right\} \), and at certain times split those particles considered more likely to lead to a trajectory that belongs to the set \(\mathscr {C}\). For example, \(\mathscr {C}\) might be the trajectories that reach some unlikely set B before hitting a likely set A, after starting in neither A nor B. In this case, the splitting will favor migration toward B. Splitting can also be used to enhance the sampling of regions that are important for a given integral. In all cases, particles which are split are given an appropriate weighting to ensure that the algorithm remains unbiased.

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Statistics and Operations ResearchUniversity of North CarolinaChapel HillUSA
  2. 2.Division of Applied MathematicsBrown UniversityProvidenceUSA

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