Heavy Hitters and Bernoulli Convolutions

A very simple event frequency approximation algorithm that is sensitive to event timeliness is suggested. The algorithm iteratively updates categorical click-distribution, producing (path of) a random walk on a standard $n$-dimensional simplex. Under certain conditions, this random walk is self-similar and corresponds to a biased Bernoulli convolution. Algorithm evaluation naturally leads to estimation of moments of biased (finite and infinite) Bernoulli convolutions.