Low-Entropy Stochastic Processes for Generating k-Distributed and Normal Sequences, and the Relationship of These Processes with Random Number Generators †
Keyword(s):
Long Run
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An infinite sequence x 1 x 2 . . . of letters from some alphabet { 0 , 1 , . . . , b - 1 } , b ≥ 2 , is called k-distributed ( k ≥ 1 ) if any k-letter block of successive digits appears with the frequency b - k in the long run. The sequence is called normal (or ∞-distributed) if it is k-distributed for any k ≥ 1 . We describe two classes of low-entropy processes that with probability 1 generate either k-distributed sequences or ∞-distributed sequences. Then, we show how those processes can be used for building random number generators whose outputs are either k-distributed or ∞-distributed. Thus, these generators have statistical properties that are mathematically proven.
The Relationship of U.S. Aid, Trade and Investment to Migration Pressures in Major Sending Countries
1982 ◽
Vol 16
(1)
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pp. 4-26
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Keyword(s):
Long Run
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Keyword(s):