Examples of Subsolutions and Their Application

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


In this chapter we present examples to illustrate the importance sampling and splitting techniques developed in Chaps.  14,  15, and  16. There are many different types of problems one might consider, and the interested reader can find additional examples in the references [76, 77, 101, 103, 105, 110, 112, 113, 116, 117]. As mentioned in Chaps.  14 and  16, an important distinction is that in the case of importance sampling, we use a smooth classical-sense subsolution, while in the case of splitting, we use a continuous but not necessarily smooth weak-sense solution. For many of the examples presented, the construction of subsolutions can be carried out in arbitrary dimension.

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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