One-dimensional uniqueness and convergence criteria for exchangeable processes (Q1103264)

If X and Y are exchangeable processes on \(I=[0,1]\) or \(R_+\); and \(X_ t\) and \(Y_ t\) have the same distribution for all t in certain infinite time-sets then, under suitable moment conditions, it is shown that \(X_ t\) and \(Y_ t\) have the same distribution for all t. The proof relies on the analytic properties of the characteristic functions of exchangeable processes. This result is used to prove the main theorem that if X, \(X_ 1\), \(X_ 2\),... are exchangeable processes on I or \(R_+\) and \(X_ n(t)\) converges in distribution to X(t) for all t in some suitable subset of I or \(R_+\) then \(X_ n\) converges in distribution to X, provided X is continuous or ergodic and satisfies certain moment conditions.