REMARKS ON THE FUNCTIONAL CENTRAL LIMIT-THEOREM FOR MARTINGALES

It is shown that filling a gap in the proof of Lemma 3 in Rootzén (1977) and using an appropriate truncation procedure one obtains general necessary conditions for the functional CLT for martingale difference arrays leading simultaneously to a solution of a remaining problem posed by Rootzén (1977). As to sufficient conditions which are weaker than previous ones in the literature Rootzén and the authors arrived independently at the result stated as Theorem 1 in the present paper. © 1979 Springer-Verlag.