Ultraslow diffusion processes under stochastic resetting

We study stochastic processes of ultraslow diffusion in the presence of instantaneous Poissonian stochastic resetting (SR). We present the analytical results which are in close agreement with the findings from computer simulations for the main standard characteristics of this SR-process, such as the mean-squared displacement (MSD), the time-averaged MSD (TAMSD), the probability-density function (PDF), and the mean first-passage time (MFPT) of the tracers. In particular, we demonstrate the nonergodicity of the ultraslow SR-process featuring MSD ≠ TAMSD, the non-Gaussianity of the resulting long-time PDF in the realized nonequilibrium stationary state, as well as the existence of an optimal reset rate minimizing the MPFT to a target. Via comparing the current results for logarithmically slow processes under SR to the main characteristics of Poissonian-reset (i) power-law fractional Brownian motion, (ii) heterogeneous-diffusion processes, and (iii) exponentially fast geometric Brownian motion, we demonstrate the universality of many key statements regarding the MSD, TAMSD, PDF, and MFPT behaviors for these mathematically very different stochastic processes under the conditions of SR.