Abstract
In this paper we investigate the Monte-Carlo method for estimation of the unknown probability of a random event on the ground of relative frequencies and under the condition that random sampling is replaced by a deterministic side input producing binary sequences of high algorithmic complexity. It is proved that if this complexity exceeds a treshold value, the sequences may be used in the Monte-Carlo methods instead of random samples as the obtained estimates converge to the estimated probability when the length of these binary sequences increases.
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