We discuss rare event simulation techniques based on state-dependent importance sampling. Classical examples and counter-examples are shown to illustrate the reach and limitations of the state-independent approach. State-dependent techniques are helpful to deal with these limitations. These techniques can be applied to both light and heavy tailed systems and often are based on subsolutions to an associated Isaacs equation and on Lyapunov bounds.
['Jose H. Blanchet', 'Henry Lam']
Rare event simulation techniques