A CENTRAL-LIMIT-THEOREM FOR WEIGHTED AND INTEGRATED MARTINGALES

We prove in this paper a central limit theorem for weighted martingale s. The method adopted involves showing the convergence of an appropria te sequence of two-parameter random processes. The desired result is o btained as a special case on the diagonal. A parallel result for integ rated martingales is then obtained using integration by parts. Example s are given to show where this theorem is needed and applicable to yie ld central limit theorems of various kinds.