Статистическое моделирование решений стохастических дифференциальных уравнений и систем со случайной структурой

The problems of constructing effective algorithms for statistical modeling of systems with a random structure given by stochastic differential equations (SDEs) are considered. For the numerical solution of the SDEs asymptotically unbiased numerical methods are constructed that are most effective for solving rigid and oscillating SDEs systems. For the modeling of inhomogeneous Poisson ensembles, algorithms with less the complexity of realizing are built up by reducing the number of calls to the pseudorandom number generator. The developed algorithms are used for statistical modeling of systems with a random structure. Questions of convergence and conditional optimization of constructed algorithms are investigated. Verification of the developed methods and their comparison with known algorithms were carried out on the solution of applied and test problems.
For specialists in computational mathematics and mathematical modeling, as well as for students of mathematical faculties