Large deviations for high minima of Gaussian processes with nonnegatively correlated increments

Zachary Selk

Statistics & Probability Letters, 2024, vol. 206, issue C

Abstract: In this article we prove large deviations principles for high minima of Gaussian processes with nonnegatively correlated increments on arbitrary intervals. Furthermore, we prove large deviations principles for the increments of such processes on intervals [a,b] where b−a is either less than the increment or twice the increment, assuming stationarity of the increments. As a chief example, we consider fractional Brownian motion and fractional Gaussian noise for H≥1/2.

Keywords: Large deviations; Gaussian processes (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spl.2023.110001

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