The Beveridge-Nelson decomposition and limit theorems for random linear processes and fields

In the talk we demonstrate the usefulness of the so-called Beveridge-Nelson decomposition in asymptotic analysis of sums of values of linear processes and fields. We consider several generalizations of this decomposition and discuss advantages and shortcomings of this approach which can be considered as one of possible methods to deal with sums of dependent random variables. This decomposition is derived for linear processes and fields with the continuous time (space) argument. The talk is based on several papers, among them [V. Paulauskas, J. Multivar. Anal. 101, (2010), 621-639] and [Yu. Davydov and V. Paulauskas, Teor. Verojat. Primenen., (2012), to appear].