Persistence probabilities in centered, stationary, Gaussian processes in discrete time

@article{Krishna2016PersistencePI,
  title={Persistence probabilities in centered, stationary, Gaussian processes in discrete time},
  author={M. Krishna and Manjunath Krishnapur},
  journal={Indian Journal of Pure and Applied Mathematics},
  year={2016},
  volume={47},
  pages={183-194}
}
Lower bounds for persistence probabilities of stationary Gaussian processes in discrete time are obtained under various conditions on the spectral measure of the process. Examples are given to show that the persistence probability can decay faster than exponentially. It is shown that if the spectral measure is not singular, then the exponent in the persistence probability cannot grow faster than quadratically. An example that appears (from numerical evidence) to achieve this lower bound is… Expand
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