Central Limit Theorem with Exchangeable Summands and Mixtures of Stable Laws as Limits
The problem of convergence in law of normed sums of exchangeable random variables is examined. First, the problem is studied w.r.t. arrays of exchangeable random variables, and the special role played by mixtures of products of stable laws - as limits in law of normed sums in different rows of the array - is emphasized. Necessary and sufficient conditions for convergence to a specific form in the above class of measures are then given. Moreover, sufficient conditions for convergence of sums in a...