CLT FOR LINEAR RANDOM FIELDS WITH STATIONARY MARTINGALE-DIFFERENCE INNOVATION

In [V. Paulauskas, On Beveridge-Nelson decomposition and limit theorems for linear random fields, J. Multivariate Anal., 101: 621-639, 2010], limit theorems for linear random fields generated by independent identically distributed innovations were proved. In this paper, we present the central limit theorem for linear random fields with martingale-differences innovations satisfying the central limit theorem from [J. Dedecker, A central limit theorem for stationary random fields, Probab. Theory Relat. Fields, 110(3): 397-426, 1998] and arranged in lexicographical order.