In this work, a versatile mathematical framework for multi-state probabilistic modeling of Resistive Switching (RS) devices is proposed for the first time. The mathematical formulation of memristor and Markov jump processes are combined and, by using the notion of master equations for finite-states, the inherent probabilistic time-evolution of RS devices is sufficiently modeled. In particular, the methodology is generic enough and can be applied for $N$ states; as a proof of concept, the proposed framework is further stressed for both two-state RS paradigm, namely $N=2$, and multi-state devices, namely $N=4$. The presented I-V results demonstrate in a qualitative and quantitative manner, adequate matching with other modeling approaches.

中文翻译：

---

基于马尔可夫跳跃过程的概率电阻开关器件建模

在这项工作中，首次提出了一种用于电阻开关 (RS) 设备多状态概率建模的通用数学框架。忆阻器和马尔可夫跳跃过程的数学公式相结合，并通过使用有限状态主方程的概念，充分模拟了 RS 设备的固有概率时间演化。特别是，该方法足够通用，可以应用于 $N$ 州；作为概念证明，所提出的框架进一步强调了两态 RS 范式，即 $N=2$ 和多态设备，即 $N=4$。所呈现的 IV 结果以定性和定量的方式证明，与其他建模方法充分匹配。