One-to-one correspondences between discrete multivariate stationary, self-similar and stationary increment fields
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909076612448256 |
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| author | Voutilainen, Marko |
| author_facet | Voutilainen, Marko |
| contents | In this article, we consider three important classes of $n$-variate fields indexed by the set of $N$ dimensional integers, namely stationary, stationary increment and self-similar fields. These classes are connected through bijective transformations. In addition, we introduce generalized AR$(1)$ type equations, whose unique stationary solutions are obtained via these transformations. Lastly, we apply the transformations in order to construct stationary fractional Ornstein-Uhlenbeck fields of the first and second kind. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_09909 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | One-to-one correspondences between discrete multivariate stationary, self-similar and stationary increment fields Voutilainen, Marko Probability 60G60, 60G10, 60G18 In this article, we consider three important classes of $n$-variate fields indexed by the set of $N$ dimensional integers, namely stationary, stationary increment and self-similar fields. These classes are connected through bijective transformations. In addition, we introduce generalized AR$(1)$ type equations, whose unique stationary solutions are obtained via these transformations. Lastly, we apply the transformations in order to construct stationary fractional Ornstein-Uhlenbeck fields of the first and second kind. |
| title | One-to-one correspondences between discrete multivariate stationary, self-similar and stationary increment fields |
| topic | Probability 60G60, 60G10, 60G18 |
| url | https://arxiv.org/abs/2401.09909 |