Link to Pubmed [PMID] – 33466050
Link to DOI – 10.1103/PhysRevE.102.062115
Phys Rev E 2020 Dec; 102(6-1): 062115
The persistence exponent θ, 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 (θ≠1/2) were obtained, but only for anomalous processes (i.e., with Hurst exponent H≠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.