Parametric analysis of stochastic oscillators by the statistical modeling method

We investigate the influence of the Wiener and the Poisson random noises on the behavior of the linear and Van der Pol oscillators with the help of the statistical modeling method. For a linear oscillator, the analytical expression of the autocovariance function of the solution to stochastic differential equation (SDE) is obtained. This expression along with the formulas of mathematical expectation and variance of the SDE solution allows us to carry out the parametric analysis and to investigate the accuracy of estimates of moments of the numerical solution to the SDE obtained with the help of the generalized Euler explicit method. For the Van der Pol oscillator, the influence of the Poisson component on the oscillation nature of the first and the second moments of the SDE solution with a large value of jumps is numerically investigated.