Abstract
The first-order linear stochastic equation $x(n+1)=ax(n)+b\xi(n), x(n)|_{n=0}=x_0$ determines the simplest kind of regression signal that is widely used in applications. The case where the right part is a non-stationary sequence has not actually been investigated. In the paper the properties of the solution of this equation are studied within the framework of the correlation theory in the case when $\xi(n)$ belongs to a particular class of random non-stationary signals, in addition, the classification is carried out using the concepts of rank or quasirank of non-stationarity. The Hilbert approach to the correlation theory of random sequences utilized in the paper allows us to study the question of the asymptotic behavior of the correlation function and makes it possible to obtain a simple inhomogeneous representation of the correlation function in terms of the correlation difference.
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