  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.
