A Negative Answer to a Problem of Aldous on Determination of Exchangeable Sequences

TL;DR

This paper investigates whether the joint distribution of exchangeable sequences can be uniquely determined by their partial sums' marginals, addressing a question posed by David Aldous and exploring related continuous and randomized problems.

Contribution

It provides a negative answer to Aldous's problem and extends the analysis to continuous time and randomized moment problems, highlighting limitations in distribution determination.

Findings

Joint distribution not always determined by partial sums' marginals

Addresses continuous time analog of Aldous's problem

Explores randomized univariate moment problem

Abstract

We present results concerning when the joint distribution of an exchangeable sequence is determined by the marginal distributions of its partial sums. The question of whether or not this determination occurs was posed by David Aldous. We then consider related uniqueness problems, including a continuous time analog to the Aldous problem and a randomized univariate moment problem.