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Persistence in a stationary time series
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 bedoi:10.1103/physreve.64.046123 pmid:11690106 fatcat:npayahnhyrdfvnzmi7jdwhwwjy