SDEX: Monte Carlo Simulation of Stochastic Differential Equations on Memristor Crossbars

Abstract: Here we present stochastic differential equations (SDEs) on a memristor crossbar, where the source of gaussian noise is derived from the random conductance due to ion drift in the devices during programming. We examine the effects of line resistance on the generation of normal random vectors, showing the skew and kurtosis are within acceptable bounds. We then show the implementation of a stochastic differential equation solver for the Black-Scholes SDE, and compare the distribution with the analytic solution. We determine that the random number generation works as intended, and calculate the energy cost of the simulation.