A scheme for the stochastization of systems of ordinary differential equations (ODEs) based on Itô calculus is presented in this article. Using the presented techniques, a system of stochastic differential equations (SDEs) can be constructed in such a way that eliminating the stochastic component yields the original system of ODEs. One of the main benefits of this scheme is the ability to construct analytical solutions to SDEs with the use of special vector-valued functions, which significantly differs from the randomization approach, which can only be applied via numerical integration. Moreover, using the presented techniques, a system of ODEs and SDEs can be constructed from a given diffusion function, which governs the uncertainty of a particular process.

中文翻译：

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两个随机微分方程组解析解的构造

本文提出了一种基于伊藤微积分的常微分方程组 (ODE) 随机化方案。使用所提出的技术，可以以消除随机分量产生原始 ODE 系统的方式构建随机微分方程 (SDE) 系统。该方案的主要优点之一是能够使用特殊的向量值函数构建 SDE 的解析解，这与只能通过数值积分应用的随机化方法有很大不同。此外，使用所提出的技术，可以根据给定的扩散函数构建 ODE 和 SDE 系统，该扩散函数控制特定过程的不确定性。