DISCRETE ALGORITHMS FOR SOLVING TWO CONTINUOUS PROBLEMS OF RANDOM
A. L. Reznik1, A. V. Tuzikov2, A. A. Soloviev1, A. V. Torgov1
1Institute of Automation and Electrometry, Siberian Branch, Russian Academy of Sciences, 630090, Russia, Novosibirsk, prosp. Akademika Koptyuga, 1
2United Institute of Informatics Problems, National Academy of Sciences, Belarus, 220012, Belarus, Minsk, ul. Surganova, 6
Keywords: случайные компактные группировки, компьютерные аналитические выкладки, обобщённые числа Каталана, random compact groups, computer-assisted analytical calculations, generalized Catalan numbers
Abstract
A combinatorial-discrete approach to solving continuous probabilistic problems arising in the analysis of random point structures is proposed. It is based on replacement of computational schemes based on calculations of cumbersome multidimensional integral expressions by schemes that do not require the use of the apparatus of differential and integral calculus. Another distinctive feature of the study is the systematic use of the generalized Catalan numbers from the multidimensional extension of the classical Catalan sequence for ranking random mutually dependent sequences.
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