Parametric analysis of the oscillatory solutions to stochastic differential equations with the Wiener and Poisson components by the Monte Carlo method

S. S. Artem’ev, M. A. Yakunin

Research output: Contribution to journalArticlepeer-review

Abstract

Using the Monte Carlo method, we address the influence of the Wiener and Poisson random noises on the behavior of oscillatory solutions to systems of stochastic differential equations (SDEs). For the linear and Van der Pol oscillators, we study the accuracy of estimates of the functionals of numerical solutions to SDEs obtained by the generalized explicit Euler method. For a linear oscillator, we obtain the exact analytical expressions for the mathematical expectation and the variance of the SDE solution. These expressions allow us to investigate the dependence of the accuracy of estimates of the solution moments on the values of SDE parameters, the size of meshsize, and the ensemble of simulated trajectories of the solution. For the Van der Pol oscillator, we study the dependence of the frequency and the damping rate of the oscillations of the mathematical expectation of SDE solution on the values of parameters of the Poisson component. The results of the numerical experiments are presented.

Original languageEnglish
Pages (from-to)157-167
Number of pages11
JournalJournal of Applied and Industrial Mathematics
Volume11
Issue number2
DOIs
Publication statusPublished - 1 Apr 2017

Keywords

  • generalized Euler method
  • Monte Carlo method
  • Poisson component
  • stochastic differential equation
  • stochastic oscillator

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