Persistence in a stationary time series - art. no. 046123

We study the persistence in a class of continuous stochastic processes that are stationary only under integer shifts of time. We show that under certa in conditions, the persistence of such a continuous process reduces to the persistence of a corresponding discrete sequence obtained from the measurem ent of the process only at integer times. We then construct a specific sequ ence for which the persistence can be computed even though the sequence is non-Markovian. We show that this may be considered as a limiting case of pe rsistence in the diffusion process on a hierarchical lattice.