Numerical solution of stochastic differential equations with random structure on supercomputers

In this paper, the accuracy of estimating the expectation of solutions to stochastic differential equations with random structure is investigated. This accuracy is shown as a function of the integration step in the generalized Euler method and the number of simulated trajectories. A drastic decrease in the accuracy at deterministic or random times of changing the SDE structure is shown by a simple equation as an example. This could be improved by the use of supercomputers for statistical modeling. The results of some numerical experiments carried out at the Siberian Supercomputer Center are presented.