The Urn of Hill, Lane and Sudderth

TL;DR

This paper reviews the properties and applications of the Hill, Lane, and Sudderth urn model, a stochastic process with memory where the probability of adding a black or white ball depends on the current composition of the urn.

Contribution

It provides a comprehensive review of the urn of Hill, Lane, and Sudderth, highlighting its key properties and various applications in stochastic processes with memory.

Findings

Characterizes the urn's probabilistic behavior

Explores applications in modeling dependent stochastic processes

Summarizes key properties and theoretical insights

Abstract

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.