An Absorbing Markov Chain Model for Stochastic Memristive Devices

Abstract

In this paper we elaborate and verify a data-driven modelling approach, pertaining to the stochastic trajectory of the memristance upon the application of pulses. Our proposed approach is to model the memristor’s behaviour as a time-homogeneous Markov chain. We introduce a simplified method that estimates the states and the state transition probabilities of the model from device measurements. We show that such a memristor model, generally corresponds to an absorbing Markov chain, the physical implications of which are also discussed. We apply this modelling methodology to real-world Pt/TiO2/Pt memristors and present results that validate its effectiveness in capturing the stochastic features of these devices over various timescales.