Fast Perfect Simulation of Vervaat Perpetutities

This work presents a faster method of simulating exactly from a distribution known as a Vervaat perpetuity. A parameter of the Vervaat perpetuity is $β\in (0,\infty)$. An earlier method for simulating from this distributon ran in time $O((2.23β)^β).$ 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 $O(β\ln(β))$ time.

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