Институт вычислительной математики
и математической геофизики

The International Conference on Computational Mathematics


Statistic modeling and Monte Carlo methods

Theoretical and Practical Solution of Problem of Random Values Generation

Antipov M.V.

Institute of Computational Mathematics and Mathematical Geophysics SB RAS (Novosibirsk)

documentstyle[12pt]{article} itle{Theoretical and Practical Solution of Problem of Random Values Generation} author{M.V.,Antipov} egin{document} maketitle egin{center} {small Institute of Computational Mathematics and Mathematical Geophysics Novosibirsk, Siberian Branch, Russian Academy of Sciences} end{center} vspace*{1mm} 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 <> values has not theoretical and even practical prospects because of inefficiency, vagueness and groundlessness. Mathematical algorithm (1) at increase of a pseudorandomness measure $mu_{ps}$ surpasses any natural realization with guarantee. The opportunity of imitation of randomness and chaos as phenomena of pseudorandomness is provided by algorithms of increasing complexity. vspace*{3mm} {small [1]. Antipov M.V. Congruent Operator in Simulation of Continuous Distributions, {it Journ. Numer. Math.}, Vol. 42, N 11, 2002, pp.1572 - 1580. [2]. Antipov M.V. {it The Restricton Principle}, Novosibirsk: Ross. Akad. Nauk, 1998, pp. 444. [3]. Antipov M.V. Multiple Congruent Convolutions of Probability Densities and Estimates in the $L^{infty}([0,1)^n)$ Space, {it Journ. Numer. Math.}, Vol. 40, N 2, 2000, pp. 293 -- 303. } end{document}

Note. Abstracts are published in author's edition

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