ON A CLASS OF NONSTATIONARY STOCHASTIC-PROCESSES

Let X(n) be a second order stochastic process with mean zero and covariance R(m, n) = EX(m)XBAR(n). A stochastic process X(n) is called stationary if R(m, n) depends only on m-n, i.e., if R(m, n) = R(m + 1, n + 1), for all m, n epsilon Z. The process X(n) is called periodically correlated with period T if R(m, n) = R(m + T, n + T) for all m, n epsilon Z. As a natural extension of these well-known stochastic processes, a linearly correlated process is defined to be one for which there exist scalars a(j) such that R(m, n) = SIGMA-j aj R(m + j, n + j), for all m, n epsilon Z. The relation between these newly defined processes with other important classes of nostationary processes is investigated. Several examples of linearly correlated processes which are not stationary, periodically correlated, or harmonizable are given.