Geodesic
On distribution of random numbers produced by sequential physical generators
Teoriâ veroâtnostej i ee primeneniâ, Tome 16 (1971) no. 2, pp. 370-378

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In certain cases, when using Monte-Carlo technique random numbers are formed by filling up a computer word (or its parts) with a piece of stationary random binary sequence (SRBS) produced by a sequential physical binary digit generator. In the paperi SRBS properties and distributions of random numbers formed in such a way are studied. It is shown that the sequence of their distribution functions converges to a continuous singular function as the length of SRBS pieces forming random numbers inreases. And this function is an eigen-function of a certain linear operator. Some properties of these functions and operators are investigated. 
@article{TVP_1971_16_2_a16,
     author = {G. A. Kozlov},
     title = {On distribution of random numbers produced by sequential physical generators},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {370--378},
     publisher = {mathdoc},
     volume = {16},
     number = {2},
     year = {1971},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1971_16_2_a16/}
}
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G. A. Kozlov. On distribution of random numbers produced by sequential physical generators. Teoriâ veroâtnostej i ee primeneniâ, Tome 16 (1971) no. 2, pp. 370-378. http://geodesic.mathdoc.fr/item/TVP_1971_16_2_a16/