State-dependent importance sampling for rare-event simulation: An overview and recent advances

This paper surveys recent techniques that have been developed for rare-event analysis of stochastic systems via simulation. We review standard (state-independent) techniques that take advantage of large deviations results for the design of efficient importance sampling estimators. Classical examples and counter-examples are discussed to illustrate the reach and limitations of the state-independent approach. Then we move to state-dependent techniques. These techniques can be applied to both light and heavy-tailed systems and are based on subsolutions (see e.g. Dupuis and Wang (2004) [5], Dupuis and Wang (2007) [6], Dupuis and Wang (2009) [80], Dupuis et al. (2007) [7]) and Lyapunov bounds (Blanchet and Glynn (2008) [9], Blanchet et al. (2007) [11], Blanchet (2009) [12]). We briefly review the ideas behind these techniques, and provide several examples in which they are applicable.