Abstract
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 presented.
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Partially supported by IMSc Project 12-R&D-IMS-5.01-0106 and UGC center for advanced studies.
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Krishna, M., Krishnapur, M. Persistence probabilities in centered, stationary, Gaussian processes in discrete time. Indian J Pure Appl Math 47, 183–194 (2016). https://doi.org/10.1007/s13226-016-0183-6
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DOI: https://doi.org/10.1007/s13226-016-0183-6