  Statistical properties of random cross-correlated sequences constructed by
the convolution method (likewise referred to as the Rice's or the inverse
Fourier transformation) are examined. Algorithms for their generation are
discussed. They are frequently reduced to solving the problem for decomposition
of the Fourier transform of the correlation matrix into a product of two
mutually conjugate matrices; different decompositions of the correlation matrix
are considered. The limits of weak and strong correlations for the one-point
probability and pair correlation functions of the sequences are studied.
Special cases of heavy-tailed distributions resulting from the convolution
generation are analyzed. Anisotropic properties of statistically homogeneous
random sequences related to asymmetry of a filtering function are discussed.
