ABSTRACT

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

中文翻译：

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统计建模方法对随机震荡器的参数分析

摘要

我们使用统计建模方法来研究维纳和泊松随机噪声对线性和Van der Pol振荡器行为的影响。在线性振荡器的情况下，获得了随机微分方程（SDE）解的自协方差函数的解析表达式。该表达式以及SDE解的数学期望和方差公式使我们能够进行参数分析，并研究基于广义显式Euler方法获得的SDE数值解的矩估计的准确性。在Van der Pol振荡器的情况下，数值研究了大跃迁下Poisson分量对SDE解的第一和第二矩振荡性质的影响。