Analysis of the accuracy of estimates of the first moments of solving SDE with Wiener and Poisson components by Monte Carlo method
Sergey Semenovich Artemiev, Mikhail Aleksandrovich Yakunin
Institute of Computational Mathematics and Mathematical Geophysics SB RAS, pr. Acad. Lavrentieva 6, Novosibirsk, Russia, 630090
Keywords: стохастические дифференциальные уравнения, винеровская и пуассоновская составляющие, метод Монте-Карло, обобщенный метод Эйлера, ансамбль траекторий, шаг интегрирования, оценки моментов, stochastic differential equations, Wiener and Poisson components, Monte Carlo method, generalized Euler method, ensemble of trajectories, integration step, estimates of moments
Abstract
In this paper, we investigate the accuracy of estimates of the first moments of a numerical solution to SDE with the Wiener and the Poisson components by the generalized Euler explicit method. The exact expressions for the mathematical expectation and variance of the test SDE solution are obtained. These expressions allow us to investigate the dependence of the accuracy of estimates obtained by Monte Carlo method on the values of SDE parameters, the size of an integration step, and the size of an ensemble of simulated trajectories of the solution. The results of the numerical experiments are presented.
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