Geodesic
On the ``reproduction'' method for simulation of random vectors and processes (randomization of correlation matrices
Teoriâ veroâtnostej i ee primeneniâ, Tome 19 (1974) no. 4, pp. 873-878

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The paper deals with a special method of simulation of random vectors with specified identical one-dimensional marginal distributions and a specified positive correlation matrix. The main idea of the method is sampling of identical random variables for each group of a random subdivision of the set of components. A simple (but not always optimal) algorithm is introduced for the determination of suitable probabilities of different subdivision variants. It is shown that the reproduction method is suitable for simulation of a stationary process with an absolutely monotone correlation function. 
@article{TVP_1974_19_4_a21,
     author = {G. A. Mikhailov},
     title = {On the ``reproduction'' method for simulation of random vectors and processes (randomization of correlation matrices},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {873--878},
     publisher = {mathdoc},
     volume = {19},
     number = {4},
     year = {1974},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1974_19_4_a21/}
}
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G. A. Mikhailov. On the ``reproduction'' method for simulation of random vectors and processes (randomization of correlation matrices. Teoriâ veroâtnostej i ee primeneniâ, Tome 19 (1974) no. 4, pp. 873-878. http://geodesic.mathdoc.fr/item/TVP_1974_19_4_a21/