Rare-Event Simulation for Stochastic Recurrence Equations with Heavy-Tailed Innovations

In this article, rare-event simulation for stochastic recurrence equations of the form [formula ommitted] is studied, where {A_n; n ≥ 1} and {B_n; n ≥ 1} are independent sequences consisting of independent and identically distributed real-valued random variables. It is assumed that the tail of the distribution of B1 is regularly varying, whereas the distribution of A1 has a suitably light tail. The problem of efficient estimation, via simulation, of quantities such as P{X_n> b} and P{sup_k=nX_k> b} for large b and n is studied. Importance sampling strategies are investigated that provide unbiased estimators with bounded relative error as b and n tend to infinity.