Normal approximation for strong demimartingales

Abstract

We consider a sequence of strong demimartingales. For these random objects, a central limit theorem is obtained by utilizing Zolotarev’s ideal metric and the fact that a sequence of strong demimartingales is ordered via the convex order with the sequence of its independent duplicates. The CLT can also be applied to demimartingale sequences with constant mean. Newman (1984) conjectures a central limit theorem for demimartingales but this problem remains open. Although the result obtained in this paper does not provide a solution to Newman’s conjecture, it is the first CLT for demimartingales available in the literature.