Probability density of the solution to nonlinear systems driven by Gaussian and Poisson white noises

IF 3 3区 工程技术 Q2 ENGINEERING, MECHANICAL
Wantao Jia , Zhe Jiao , Wanrong Zan , Weiqiu Zhu
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引用次数: 0

Abstract

A new method is proposed to compute the probability density of the multi-dimensional nonlinear dynamical system perturbed by a combined excitation of Gaussian and Poisson white noises. We first deduce a probability-density solver from the Euler–Maruyama scheme of the stochastic system and the corresponding Chapman–Kolmogorov equation. This solver actually is an explicit numerical formula of the probability density of the solution to this stochastic system. To compute the probability density, we propose an efficient algorithm for this solver, which actually is the implementation of a numerical integration. Furthermore, we prove this solver is an approximated solution of the corresponding forward Kolmogorov equation. Numerical examples are conducted to illustrate our probability-density solver.

高斯和泊松白噪声驱动的非线性系统解的概率密度
本文提出了一种新方法,用于计算受到高斯白噪声和泊松白噪声联合激励扰动的多维非线性动力系统的概率密度。我们首先从随机系统的 Euler-Maruyama 方案和相应的 Chapman-Kolmogorov 方程推导出概率密度求解器。这个求解器实际上是该随机系统解的概率密度的显式数值公式。为了计算概率密度,我们为这个求解器提出了一种高效算法,实际上就是数值积分的实现。此外,我们还证明了这种求解器是相应的正向科尔莫哥罗夫方程的近似解。我们通过数值示例来说明我们的概率密度求解器。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Probabilistic Engineering Mechanics
Probabilistic Engineering Mechanics 工程技术-工程:机械
CiteScore
3.80
自引率
15.40%
发文量
98
审稿时长
13.5 months
期刊介绍: This journal provides a forum for scholarly work dealing primarily with probabilistic and statistical approaches to contemporary solid/structural and fluid mechanics problems encountered in diverse technical disciplines such as aerospace, civil, marine, mechanical, and nuclear engineering. The journal aims to maintain a healthy balance between general solution techniques and problem-specific results, encouraging a fruitful exchange of ideas among disparate engineering specialities.
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