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Simulating Perpetuities

Author

Listed:
  • Luc Devroye

    (McGill University)

Abstract

A perpetuity is a random variable that can be represented as $$1 + W_1 + W_1 W_2 + W_1 W_2 W_3 + \cdot \cdot \cdot ,$$ , where the W i's are i.i.d. random variables. We study exact random variate generation for perpetuities and discuss the expected complexity. For the Vervaat family, in which $$W_1 \underline{\underline {\mathcal{L}}} {\text{ }}U^{1/\beta } ,\beta > 0,U$$ uniform [0, 1], all the details of a novel rejection method are worked out. There exists an implementation of our algorithm that only uses uniform random numbers, additions, multiplications and comparisons.

Suggested Citation

  • Luc Devroye, 2001. "Simulating Perpetuities," Methodology and Computing in Applied Probability, Springer, vol. 3(1), pages 97-115, March.
    • Handle: RePEc:spr:metcap:v:3:y:2001:i:1:d:10.1023_a:1011470225335
    DOI: 10.1023/A:1011470225335
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    References listed on IDEAS

    as
    1. Gary Ulrich, 1984. "Computer Generation of Distributions on the M‐Sphere," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 33(2), pages 158-163, June.
    2. Devroye, Luc, 1989. "On random variate generation when only moments or Fourier coefficients are known," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 31(1), pages 71-89.
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    Cited by:

    1. Onno Boxma & Andreas Löpker & Michel Mandjes & Zbigniew Palmowski, 2021. "A multiplicative version of the Lindley recursion," Queueing Systems: Theory and Applications, Springer, vol. 98(3), pages 225-245, August.
    2. Margarete Knape & Ralph Neininger, 2008. "Approximating Perpetuities," Methodology and Computing in Applied Probability, Springer, vol. 10(4), pages 507-529, December.
    3. Margarete Knape & Ralph Neininger, 2013. "Appendix to “Approximating Perpetuities”," Methodology and Computing in Applied Probability, Springer, vol. 15(3), pages 707-712, September.

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