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Numerical Analysis and Applications

2016 year, number 3

Using a randomized method of a maximum cross-section for simulating random structure systems with distributed transitions

Tat'yana Aleksandrovna Averina1,2
1Institute of Computational Mathematics and Mathematical Geophysics SB RAS, pr. Acad. Lavrentieva 6, Novosibirsk, 630090, Russia
2Novosibirsk State University, Pirogova st., 2, Novosibirsk, 630090, Russia
Keywords: статистическое моделирование, системы со случайной структурой, стохастические дифференциальные уравнения, пуассоновский поток, метод В«максимального сеченияВ», statistical simulation, systems with a random structure, stochastic differential equations, Poisson flow, numerical methods, maximum cross-section method


In this paper we consider the random structure systems with distributed transitions. A theorem about the form of conditional structure distributions has been proved. To simulatethese distributions a statistical algorithm using a randomized method of maximum cross-section is constructed. Also, a modified version of this algorithm using the simulation of one random number has been constructed. The algorithms developed were used for the simulation of the numerical solution of random structure systems with distributed transitions. The theorem about a weak convergence of the numerical solution, obtained by the algorithms developed has been proved.