In this section, spectrally correlated stochastic processes are introduced (Definitions 4.2.4–4.2.8) and characterized (Theorems 4.2.7 and 4.2.9). Moreover, examples of applications where such processes occur are presented.
Definition 4.2.1 A covariance function is said to be harmonizable if there exists a spectral covariance function of bounded variation on
where the integral is a Fourier-Stieltjes transform (Loève 1963).
Definition 4.2.2 A second-order stochastic process is said to be (strongly) harmonizable if there exists a second-order stochastic process χ(f) with increments dχ(f) having covariance function with of bounded variation on such that
with probability one ...