### ?

## Nonstationary distributions and relaxation times in a stochastic model of memristor

We propose a stochastic model for a memristive system by

generalizing known approaches and experimental results. We validate our

theoretical model by experiments carried out on a memristive device based

on Au/Ta/ZrO2(Y)/Ta2O5/TiN/Ti multilayer structure. In the framework

of the proposed model we obtain the exact analytic expressions for stationary

and nonstationary solutions. We analyze the equilibrium and non-equilibrium

steady-state distributions of the internal state variable of the memristive system

and study the influence of fluctuations on the resistive switching, including the

relaxation time to the steady-state. The relaxation time shows a nonmonotonic

dependence, with a minimum, on the intensity of the fluctuations. This paves

the way for using the intensity of fluctuations as a control parameter for

switching dynamics in memristive devices.