Analysis of estimation accuracy of the first moments of a Monte Carlo solution to an SDE with Wiener and Poisson components

• Published in: Numerical analysis and applications Vol. 9; no. 1; pp. 24 - 33
• Main Authors: Artemiev, S. S., Yakunin, M. A.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 2016
• Subjects: Mathematics; Mathematics and Statistics; Numerical Analysis; Monte Carlo method; estimators of moments; generalized Euler method; integration step; stochastic differential equations; ensemble of trajectories; Wiener and Poisson components
• ISSN: 1995-4239; 1995-4247
• DOI: 10.1134/S1995423916010031

In this paper, the estimation accuracy of the first moments of a numerical solution to an SDE with Wiener and Poisson components is investigated by a generalized explicit Euler method. Exact expressions for the mathematical expectation and variance of a test SDE solution are obtained. These expressions allow us to investigate the estimation accuracy obtained by a Monte Carlo method versus the SDE parameters, the integration step, and the size of the ensemble of simulated trajectories of the solution. The results of test numerical experiments are presented.