Statistic modeling and Monte Carlo methods
documentstyle[12pt]{article}
itle{Theoretical and Practical Solution of Problem
of Random Values Generation}
author{M.V.,Antipov}
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maketitle
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{small
Institute of Computational Mathematics and Mathematical
Geophysics
Novosibirsk, Siberian Branch, Russian Academy of Sciences}
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In work [1,2] is proven, that the solution of a randomness problem
it is impossible outside of modernization of a mathematical views
on the basis of the concept of the restriction principle. It concerns
and modeling of random numbers to the full. Traditional way of randomness
imitation uses separate algorithms $ALG_i$,. They possess quite
evaluated but insuperable defects. For this reason even the physical
algorithms are pseudorandom [1,2] and have a finite measure
of pseudorandomness $mu_{ps} (ALG_i)$,.
At the same time as is shown in [3] the operator of congruent
summation
$$
z_{(m)}^{(n)} equiv left{,sumlimits_{i=1}^{m+1},y_i^{(n)},
ight}({
m mod},1),, quad y_i^{(n)} = left(,x_i^{(1)},,
x_i^{(2)},,...,,x_i^{(n)},
ight),, eqno{(1)}
$$
brings in sharp increase of a measure of pseudorandomness
$mu_{ps}{z_{(m)}^{(n)}} stackrel{m o infty}{Longrightarrow} infty$ for resulting algorithm $ALG(m)$
in parallel with all characteristics.
{f Lemma.} At increase of summation's parameter $m$ and
fulfilment some easily achievable conditions with decrease of
algorithmical dependence $ALG_i$,, the pseudorandomness
measure $mu_{ps} {ALG (m)}$ exceeds any given size.
{f Theorem.} The opportunity of numerical modeling $z_{(m)}^{(n)}$
of unlimitely increasing pseudorandomness measure $mu_{ps}$
permits the problem of randomness.
Thus, the imitation of randomness with the help of natural or any other
processes is impossible, and the physical generation so named <
Note. Abstracts are published in author's edition
© 1996-2000, Siberian Branch of Russian Academy of Sciences, Novosibirsk
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