Probabilistic Resistive Switching Device modeling based on Markov Jump processes

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.