On the Importance Function in splitting simulation

Marnix J.J. Garvels, Jan C.W. van Ommeren, Dirk P. Kroese

Research output: Contribution to journalArticleAcademicpeer-review

56 Citations (Scopus)
12 Downloads (Pure)


The splitting method is a simulation technique for the estimation of very small probabilities. In this technique, the sample paths are split into multiple copies, at various stages in the simulation. Of vital importance to the efficiency of the method is the Importance Function (IF). This function governs the placement of the thresholds or surfaces at which the paths are split We derive a characterisation of the optimal IF and show that for multi-dimensional models the natural choice for the IF is usually not optimal. We also show how nearly optimal splitting surfaces can be derived or simulated using reverse time analysis. Our numerical experiments illustrate that by using the optimal IF, one can obtain a significant improvement in simulation efficiency.
Original languageEnglish
Pages (from-to)363-371
Number of pages9
JournalEuropean transactions on telecommunications
Issue number4
Publication statusPublished - Jul 2002


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