This paper is devoted to study random linear control systems where the initial condition, the final target, and the elements of matrices defining the coefficients are random variables, while the control is a stochastic process. The so-called Random Variable Transformation technique is adapted to obtain closed-form expressions of the probability density functions of the solution and of the control. The theoretical findings are applied to study the dynamics of a damped oscillator subject to parametric noise.

中文翻译：

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求解完全随机的一阶线性控制系统：在研究随机控制下带参数噪声的阻尼振荡器的动力学中的应用

本文致力于研究随机线性控制系统，其中初始条件，最终目标以及定义系数的矩阵元素是随机变量，而控制则是随机过程。所谓的随机变量变换技术适于获得解和控制的概率密度函数的闭合形式的表达式。将理论发现应用于研究受参数噪声影响的阻尼振荡器的动力学。