Exact simulation of generalised Vervaat perpetuities

Angelos Dassios, Yan Qu*, Jia Wei Lim

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

8 Citations (Scopus)
148 Downloads (Pure)


We consider a generalised Vervaat perpetuity of the form X = Y 1 W 1 +Y 2 W 1 W 2 + · · ·, where and (Y i) i≥0 is an independent and identically distributed sequence of random variables independent from (W i) i≥0. Based on a distributional decomposition technique, we propose a novel method for exactly simulating the generalised Vervaat perpetuity. The general framework relies on the exact simulation of the truncated gamma process, which we develop using a marked renewal representation for its paths. Furthermore, a special case arises when Y i = 1, and X has the generalised Dickman distribution, for which we present an exact simulation algorithm using the marked renewal approach. In particular, this new algorithm is much faster than existing algorithms illustrated in Chi (2012), Cloud and Huber (2017), Devroye and Fawzi (2010), and Fill and Huber (2010), as well as being applicable to the general payments case. Examples and numerical analysis are provided to demonstrate the accuracy and effectiveness of our method.

Original languageEnglish
Pages (from-to)57-75
Number of pages19
JournalJournal of Applied Probability
Issue number1
Publication statusPublished - 12 Jul 2019


  • Dickman distribution
  • exact simulation
  • marked renewal process
  • truncated gamma process
  • Vervaat perpetuity


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