Geodesic
On Multi-Dimensional Stationary Random Processes
Teoriâ veroâtnostej i ee primeneniâ, Tome 3 (1958) no. 4, pp. 458-462

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The necessary and sufficient conditions for the regularity as well as for “the maximum regularity” of $n$-dimensional stationary random processes $(x_1(t),x_2(t),\dots,x_n(t))$ with continuous time are obtained. Wold’s development “for the process” is also proved. 
@article{TVP_1958_3_4_a6,
     author = {E. G. Gladyshev},
     title = {On {Multi-Dimensional} {Stationary} {Random} {Processes}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {458--462},
     publisher = {mathdoc},
     volume = {3},
     number = {4},
     year = {1958},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1958_3_4_a6/}
}
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E. G. Gladyshev. On Multi-Dimensional Stationary Random Processes. Teoriâ veroâtnostej i ee primeneniâ, Tome 3 (1958) no. 4, pp. 458-462. http://geodesic.mathdoc.fr/item/TVP_1958_3_4_a6/