Large Deviations for High Minima of Gaussian Processes with Nonnegatively Correlated Increments
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866916193577730048 |
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| author | Selk, Zachary |
| author_facet | Selk, Zachary |
| contents | 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 $H\geq 1/2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2103_04501 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Large Deviations for High Minima of Gaussian Processes with Nonnegatively Correlated Increments Selk, Zachary Probability 60G15, 60G22, 60K25, 60G55, 60F10 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 $H\geq 1/2$. |
| title | Large Deviations for High Minima of Gaussian Processes with Nonnegatively Correlated Increments |
| topic | Probability 60G15, 60G22, 60K25, 60G55, 60F10 |
| url | https://arxiv.org/abs/2103.04501 |