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.
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Devroye, L. Simulating Perpetuities. Methodology and Computing in Applied Probability 3, 97–115 (2001). https://doi.org/10.1023/A:1011470225335
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DOI: https://doi.org/10.1023/A:1011470225335