Multidimensional random processes with normal covariances

where R(*) is a weakly stationary covariance. Thanks to the facts that R(s, s) ^ 0 for every seU1 and R (0) ^ 0 this definition yields R(s) !> 0 for every s e (R__. The definition of local stationarity for random sequences is given in [4]. In this case a covariance function R(-, •), defined on Z x Z (Cartesian product of integers), can be expressed as R(n, m) = R(n + m) R(n m) where R(*) is a stationary covariance. Here, the function R(«) need not be nonnegative. Under assumption of continuity of R('), R(*) and nonnegative-definite property of R(*), in the case of a random process, the corresponding locally stationary covariance function can be written in the form