A Central Limit Theorem, and related results, for a two-color randomly reinforced urn

TL;DR

This paper establishes a Central Limit Theorem for the composition of a two-color randomly reinforced urn, demonstrating that the limiting distribution is continuous with no point masses, advancing understanding of reinforced urn models.

Contribution

The paper proves a CLT for two-color reinforced urns and shows the limit distribution is continuous, providing new theoretical insights into urn composition behavior.

Findings

Proves a CLT for the urn composition sequence.

Shows the limit distribution has no point masses.

Enhances understanding of reinforced urn asymptotics.

Abstract

We prove a Central Limit Theorem for the sequence of random compositions of a two-color randomly reinforced urn. As a consequence, we are able to show that the distribution of the urn limit composition has no point masses.