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Exact simulation of generalised Vervaat perpetuities

Dassios, Angelos ORCID: 0000-0002-3968-2366, Lim, Jia Wei and Qu, Yan (2019) Exact simulation of generalised Vervaat perpetuities. Journal of Applied Probability, 56 (1). pp. 57-75. ISSN 0021-9002

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Identification Number: 10.1017/jpr.2019.6


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.

Item Type: Article
Official URL:
Additional Information: © 2019 Cambridge University Press
Divisions: Statistics
Subjects: Q Science > QA Mathematics
Date Deposited: 03 Jan 2019 15:56
Last Modified: 11 Jul 2024 17:51

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