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arXiv · 1710.05777

Persistence probabilities of two-sided (integrated) sums of correlated stationary Gaussian sequences

Frank Aurzada·Micha Buck
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Abstract

We study the persistence probability for some two-sided discrete-time Gaussian sequences that are discrete-time analogs of fractional Brownian motion and integrated fractional Brownian motion, respectively. Our results extend the corresponding ones in continuous-time in [Molchan, Commun. Math. Phys., 1999] and [Molchen, J. Stat. Phys., 2017] to a wide class of discrete-time processes.

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Frank Aurzada, Micha Buck. 2017-10-16. Persistence probabilities of two-sided (integrated) sums of correlated stationary Gaussian sequences. https://doi.org/10.1007/s10955-018-1954-8

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