Importance sampling of heavy-tailed iterated random functions

Bohan Chen, Chang-Han Rhee, Bert Zwart

Research output: Contribution to journalArticlepeer-review


We consider the stationary solution Z of the Markov chain {Zn}n∈N defined by Zn+1 = Ψn+1(Zn), where {Ψn}n∈N is a sequence of independent and identically distributed random Lipschitz functions. We estimate the probability of the event {Z > x} when x is large, and develop a state-dependent importance sampling estimator under a set of assumptions on Ψn such that, for large x, the event {Z > x} is governed by a single large jump. Under natural conditions, we show that our estimator is strongly efficient. Special attention is paid to a class of perpetuities with heavy tails.

Original languageEnglish (US)
Pages (from-to)805-832
Number of pages28
JournalAdvances in Applied Probability
Issue number3
StatePublished - Sep 1 2018


  • State-dependent importance sampling
  • heavy-tailed distribution
  • iterated random function
  • perpetuities

ASJC Scopus subject areas

  • Statistics and Probability
  • Applied Mathematics


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