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 ∈ (0,∞). 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.