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| Main Author: | |
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| Format: | Preprint |
| Published: |
2020
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2010.14901 |
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Table of Contents:
- An algorithm is presented that, taking a sequence of independent Bernoulli random variables with parameter $1/2$ as inputs and using only rational arithmetic, simulates a Bernoulli random variable with possibly irrational parameter $τ$. It requires a series representation of $τ$ with positive, rational terms, and a rational bound on its truncation error that converges to $0$. The number of required inputs has an exponentially bounded tail, and its mean is at most $3$. The number of arithmetic operations has a tail that can be bounded in terms of the sequence of truncation error bounds. The algorithm is applied to two specific values of $τ$, including Euler's constant, for which obtaining a simple simulation algorithm was an open problem.