Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

The central limit theorem for m-dependent variables asymptotically stationary to second order

P. H. Dianandaa1

a1 Department of Mathematics University of Malaya

In a recent paper (3) the Lindeberg-Lévy theorem (2) was extended for certain types of stationary dependent variables. In the present paper mainly the same basic ideas as were used in (3) are employed to give central limit theorems for m-dependent scalar variables (a) stationary to second order and (b) asymptotically stationary to second order, the sufficient condition in each case being akin to the Linde-berg condition ((1), p. 57) for independent variables. The analogue of the main theorem for vector variables is given. An extension of the Lindeberg-Lévy theorem is derived.

(Received July 02 1953)

(Revised August 20 1953)