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We consider Monte Carlo algorithms for computing an integral θ=∫fdπ which is positive but can be arbitrarily close to 0. It is assumed that we can generate a sequence Xn of uniformly bounded random variables with expectation θ. Estimator θˆ=θˆ(X1,X2,…,XN) is called an (ε,α)-approximation if it has fixed relative precision ε at a given level of confidence 1−α, that is it satisfies P(|θˆ−θ|≤εθ)≥1−α...
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