Self-similar Gaussian Markov processes
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866918123113807872 |
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| author | Bauer, Benedict Gerhold, Stefan |
| author_facet | Bauer, Benedict Gerhold, Stefan |
| contents | We characterize all multi-dimensional real self-similar Gaussian Markov processes. Three types of covariance matrix functions occur: white-noise type functions, covariances that can be expressed by continuous matrix semigroups, and covariances based on non-continuous solutions of Cauchy's functional equation. Characterizing the latter requires us to develop some results on the representation theory of non-continuous matrix semigroups, which are presented in a companion paper. In dimension one, besides white noise, the self-similar Gaussian Markov processes reduce to a two-parameter family of time-changed Brownian motions. This observation simplifies several proofs of non-Markovianity of concrete processes found in the literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2008_03052 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Self-similar Gaussian Markov processes Bauer, Benedict Gerhold, Stefan Probability 60G15 (Primary) 60G18, 60G22, 39B22, 47D03, 15A16 (Secondary) We characterize all multi-dimensional real self-similar Gaussian Markov processes. Three types of covariance matrix functions occur: white-noise type functions, covariances that can be expressed by continuous matrix semigroups, and covariances based on non-continuous solutions of Cauchy's functional equation. Characterizing the latter requires us to develop some results on the representation theory of non-continuous matrix semigroups, which are presented in a companion paper. In dimension one, besides white noise, the self-similar Gaussian Markov processes reduce to a two-parameter family of time-changed Brownian motions. This observation simplifies several proofs of non-Markovianity of concrete processes found in the literature. |
| title | Self-similar Gaussian Markov processes |
| topic | Probability 60G15 (Primary) 60G18, 60G22, 39B22, 47D03, 15A16 (Secondary) |
| url | https://arxiv.org/abs/2008.03052 |