2015/01/25 by Takis Konstantopoulos, Konstantopoulos, Takis, Linglong Yuan +1
Computer Science · Economics, Econometrics and Finance · Mathematics · #28A35 #28C05 (Primary) #28C15 (Secondary) #46B99 #60G09 #62F15 #Bayesian Methods and Mixture Models #FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR) #Stochastic processes and financial applications #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.1501.06188
openalex publication_date 2015/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A length-n random sequence X1,…,Xn in a space S is finitely exchangeable if its distribution is invariant under all n! permutations of coordinates. Given N > n, we study the extendibility problem: when is it the case that there is a length-N exchangeable random sequence Y1,…, YN so that (Y1,…,Yn) has the same distribution as (X1,…,Xn)? In this paper, we give a necessary and sufficient condition so that, for given n and N, the extendibility problem admits a solution. This is done by employing functional-analytic and measure-theoretic arguments that take into account the symmetry. We also address the problem of infinite extendibility. Our results are valid when X1 has a regular distribution in a locally compact Hausdorff space S. We also revisit the problem of representation of the distribution of a finitely exchangeable sequence.