We introduce an approach based on the Chapman-Kolmogorov equation to model heterogeneous probabilistic circuits, namely, the circuits combining binary or multi-state probabilistic memristive devices and continuum reactive components (capacitors and/or inductors). Such circuits are described in terms of occupation probabilities of memristive states that are functions of reactive variables. As an illustrative example, the series circuit of a binary memristor and capacitor is considered in detail. Some analytical solutions are found. Our work offers a novel analytical/numerical tool for modeling complex probabilistic networks, which may find a broad range of applications.

中文翻译：

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具有概率忆阻器件的异构电路理论

我们引入一种基于Chapman-Kolmogorov方程的方法来对异构概率电路建模，即，将二元或多态概率忆阻器件与连续电抗组件（电容器和/或电感器）组合在一起的电路。根据忆阻态的占有概率描述了这样的电路，忆阻态是电抗变量的函数。作为说明性示例，详细考虑了二进制忆阻器和电容器的串联电路。找到了一些分析解决方案。我们的工作为建模复杂的概率网络提供了一种新颖的分析/数值工具，可能会找到广泛的应用。