Survival Probability Dynamics of Scaled Brownian Motion: Effect of Nonstationary Property

Scaled Brownian motion (SBM) is a popular model of nonstationary anomalous diffusion process. We here extend the SBM model to investigate the survival probability of stationary anomalous diffusion process. By making comparison between the SBM model and the stationary SBM model, we investigate the effect of stationarity on the first passage kinetics. A non stationary scaled Brownian motion (SBM) is slower than the stationary SBM in searching for specific targets when motion is subdiffusive. However, the former is faster than the latter when motion is super diffusive.