Approximating martingales and the central limit theorem for strictly stationary processes

AbstractThe proofs of various central limit theorems for strictly stationary sequences of random variables are based on approximating the partial sums of the process by martingales (cf., e.g., Gordin, 1969; Dürr and Goldstein, 1984; or Hall and Heyde, 1980, Chapter 5). Here we shall give a study on the assumptions of such theorems and introduce new ones. Then we shall discuss conditions under which the results take place in almost all ergodic components simultaneously and present an application to the limit theory of stationary linear proceses with random coefficients