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

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  • Mendo, Luis

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.

Suggested Citation

  • Mendo, Luis, 2019. "An asymptotically optimal Bernoulli factory for certain functions that can be expressed as power series," Stochastic Processes and their Applications, Elsevier, vol. 129(11), pages 4366-4384.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:11:p:4366-4384
    DOI: 10.1016/j.spa.2018.11.017
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