A Look At Multilevel Splitting

  • Paul Glasserman
  • Philip Heidelberger
  • Perwez Shahabuddin
  • Tim Zajic
Part of the Lecture Notes in Statistics book series (LNS, volume 127)


This paper gives a non-technical overview of our work on the efficiency of a simple multilevel splitting technique for estimating rare event probabilities. For a particular class of stochastic models, this method is asymptotically optimal provided the splitting factor is properly chosen. However, for more general classes of processes, the method fails to be asymptotically optimal unless the splitting is done in a manner consistent with the dominant way in which the rare event happens (the large deviations behavior). In the absence of such consistency, the method also exhibits a kind of bias in which the estimate is too small with high probability. We briefly contrast our approach with one used in nuclear physics.


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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Paul Glasserman
    • 1
  • Philip Heidelberger
    • 2
  • Perwez Shahabuddin
    • 3
  • Tim Zajic
    • 3
  1. 1.Columbia Business SchoolNew YorkUSA
  2. 2.IBM Research DivisionT.J. Watson Research CenterYorktown HeightsUSA
  3. 3.IEOR DepartmentColumbia UniversityNew YorkUSA

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