Persistence in a stationary time series

Satya N. Majumdar, Deepak Dhar
2001 Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics  
We study the persistence in a class of continuous stochastic processes that are stationary only under integer shifts of time. We show that under certain conditions, the persistence of such a continuous process reduces to the persistence of a corresponding discrete sequence obtained from the measurement of the process only at integer times. We then construct a specific sequence for which the persistence can be computed even though the sequence is non-Markovian. We show that this may be
more » ... as a limiting case of persistence in the diffusion process on a hierarchical lattice.
doi:10.1103/physreve.64.046123 pmid:11690106 fatcat:npayahnhyrdfvnzmi7jdwhwwjy