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

摘要

In this article, rare-event simulation for stochastic recurrence equations of the form X_(n+1) = A_(n+1)X_n + B_(n+1), X_0 = 0 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 B_1 is regularly varying, whereas the distribution of A_1 has a suitably light tail. The problem of efficient estimation, via simulation, of quantities such as P{X_n ≥ b} and P{sup_(k≤n) X_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.