This article is cited in 5 papers

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

T. A. Averina<sup>ab

a</sup> Novosibirsk State University, Pirogova st., 2, Novosibirsk, 630090, Russia
^b Institute of Computational Mathematics and Mathematical Geophysics SB RAS, 6 Lavrentiev pr., Novosibirsk, 630090, Russia

Abstract: 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.

Key words: statistical simulation, systems with a random structure, stochastic differential equations, Poisson flow, numerical methods, maximum cross-section method.

UDC: 519.676

Received: 30.10.2015
Revised: 03.12.2015

DOI: 10.15372/SJNM20160301

 English version: Numerical Analysis and Applications, 2016, 9:3, 179–190

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