The Urn of Hill, Lane and Sudderth

We review some facts, properties and applications of the urn of Hill, Lane and Sudderth, a paradigmatic model of stochastic process with memory, where the urn evolution is as follows: consider an urn of given capacity, at each step a new ball, black or white, is added to the urn with probability that is function (urn function) of the fraction of black balls. The process runs until capacity is reached.