Large Deviations for High Minima of Gaussian Processes with Nonnegatively Correlated Increments

Statistics and Probability Letters 206 (C). March 2024 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...

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Bibliographic Details
Main Author Selk, Zachary
Format Journal Article
LanguageEnglish
Published 07.03.2021
Subjects
Mathematics - Probability
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Summary:Statistics and Probability Letters 206 (C). March 2024 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 $H\geq 1/2$.
DOI:10.48550/arxiv.2103.04501