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arXiv · 1510.01780

Fast Perfect Simulation of Vervaat Perpetutities

Kirkwood Cloud·Mark Huber
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Abstract

This work presents a faster method of simulating exactly from a distribution known as a Vervaat perpetuity. A parameter of the Vervaat perpetuity is $\beta \in (0,\infty)$. An earlier method for simulating from this distributon ran in time $O((2.23\beta)^{\beta}).$ This earlier method utilized dominated coupling from the past that bounded a stochastic process for perpetuities from above. By extending to non-Markovian update functions, it is possible to create a new method that bounds the perpetuities from both above and below. This new approach is shown to run in $O(\beta \ln(\beta))$ time.

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Kirkwood Cloud, Mark Huber. 2015-10-06. Fast Perfect Simulation of Vervaat Perpetutities. https://arxiv.org/abs/1510.01780

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