An asymptotically optimal Bernoulli factory for certain functions that can be expressed as power series

Luis Mendo

Stochastic Processes and their Applications, 2019, vol. 129, issue 11, 4366-4384

Abstract: Given a sequence of independent Bernoulli variables with unknown parameter p, and a function f expressed as a power series with non-negative coefficients that sum to at most 1, an algorithm is presented that produces a Bernoulli variable with parameter f(p). In particular, the algorithm can simulate f(p)=pa, a∈(0,1). For functions with a derivative growing at least as f(p)∕p for p→0, the average number of inputs required by the algorithm is asymptotically optimal among all simulations that are fast in the sense of Nacu and Peres. A non-randomized version of the algorithm is also given. Some extensions are discussed.

Keywords: Bernoulli factory; Simulation; Power series (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:129:y:2019:i:11:p:4366-4384

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DOI: 10.1016/j.spa.2018.11.017

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