A CENTRAL-LIMIT-THEOREM FOR WEIGHTED AND INTEGRATED MARTINGALES

We prove in this paper a central limit theorem for weighted martingales. The method adopted involves showing the convergence of an appropriate sequence of two-parameter random processes. The desired result is obtained as a special case on the diagonal. A parallel result for integrated martingales is then obtained using integration by parts. Examples are given to show where this theorem is needed and applicable to yield central limit theorems of various kinds.