Geodesic
Simple Monte Carlo integration with respect to Bernoulli convolutions
Applications of Mathematics, Tome 57 (2012) no. 6, pp. 617-626

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We apply a Markov chain Monte Carlo method to approximate the integral of a continuous function with respect to the asymmetric Bernoulli convolution and, in particular, with respect to a binomial measure. This method---inspired by a cognitive model of memory decay---is extremely easy to implement, because it samples only Bernoulli random variables and combines them in a simple way so as to obtain a sequence of empirical measures converging almost surely to the Bernoulli convolution. We give explicit bounds for the bias and the standard deviation for this approximation, and present numerical simulations showing that it outperforms a general Monte Carlo method using the same number of Bernoulli random samples.
DOI : 10.1007/s10492-012-0037-4
Classification : 60G57, 65C05, 65D30
Keywords: MCMC; Bernoulli convolution; binomial measure; Monte Carlo integration; empirical measures 
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Gómez, David M.; Dartnell, Pablo. Simple Monte Carlo integration with respect to Bernoulli convolutions. Applications of Mathematics, Tome 57 (2012) no. 6, pp. 617-626. doi: 10.1007/s10492-012-0037-4

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