Examples of Subsolutions and Their Application

Abstract

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.