On a new family of weighted Gaussian processes: an application to bat telemetry data
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866915547129577472 |
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| author | Gonzalez, Jose Hermenegildo Ramirez Salas, Antonio Murillo Sun, Ying |
| author_facet | Gonzalez, Jose Hermenegildo Ramirez Salas, Antonio Murillo Sun, Ying |
| contents | In this article we use a covariance function that arises from limit of fluctuations of the rescaled occupation time process of a branching particle system, to introduce a family of weighted long-range dependence Gaussian processes. In particular, we consider two subfamilies for which we show that the process is not a semimartingale, that the processes exhibit long-range dependence and have long-range memory of logarithmic order. Finally, we illustrate that this family of processes is useful for modeling real world data. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_19903 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a new family of weighted Gaussian processes: an application to bat telemetry data Gonzalez, Jose Hermenegildo Ramirez Salas, Antonio Murillo Sun, Ying Probability Statistics Theory 60G15, 62M09 In this article we use a covariance function that arises from limit of fluctuations of the rescaled occupation time process of a branching particle system, to introduce a family of weighted long-range dependence Gaussian processes. In particular, we consider two subfamilies for which we show that the process is not a semimartingale, that the processes exhibit long-range dependence and have long-range memory of logarithmic order. Finally, we illustrate that this family of processes is useful for modeling real world data. |
| title | On a new family of weighted Gaussian processes: an application to bat telemetry data |
| topic | Probability Statistics Theory 60G15, 62M09 |
| url | https://arxiv.org/abs/2405.19903 |