Anomalous persistence exponents for normal yet aging diffusion

The persistence exponent theta, which characterizes the long-time decay of the survival probability of stochastic processes in the presence of an absorbing target, plays a key role in quantifying the dynamics of fluctuating systems. So far, anomalous values of the persistence exponent (theta not equal 1/2) were obtained, but only for anomalous processes (i.e., with Hurst exponent H not equal 1/2). Here we exhibit examples of ageing processes which, even if they display asymptotically a normal diffusive scaling (H = 1/2), are characterized by anomalous persistent exponents that we determine analytically. Based on this analysis, we propose the following general criterion: The persistence exponent of asymptotically diffusive processes is anomalous if the increments display ageing and depend on the observation time T at all timescales.