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

M. Krishna () and Manjunath Krishnapur ()
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M. Krishna: The Institute of Mathematical Sciences
Manjunath Krishnapur: Indian Institute of Science

Indian Journal of Pure and Applied Mathematics, 2016, vol. 47, issue 2, 183-194

Abstract: 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.

Keywords: Persistence probability; hole probability; gap probability; stationary Gaussian process; spectral measure (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s13226-016-0183-6

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