The Sequences with Stationary differences

Abstract

This paper studies nonstationary random sequences with stationary increments. General representations are obtained for their correlation function and correlation differences. The general case is studied for non-stationary sequence, which is the solution of difference equation with stationary right-hand side. Derived spectral representations prove that such sequences are harmonizable. The general representation of solution correlation function is obtained for equation, the right-hand side of which is a non-stationary sequence of finite non-stationarity rank.