Characterization of continuous stationary fields as generalized Ornstein-Uhlenbeck fields via multi-parameter Langevin equation and multiple Riemann-Stieltjes integration
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911545671286784 |
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| author | Voutilainen, Marko Ilmonen, Pauliina Viitasaari, Lauri |
| author_facet | Voutilainen, Marko Ilmonen, Pauliina Viitasaari, Lauri |
| contents | In this article, we characterize continuous stationary fields via generalized Langevin dynamics. This gives natural connections between stationary fields, stationary increment fields, self-similar fields, and generalized Langevin dynamics. Our contribution extends some recently proved similar results for stochastic processes to the case of continuous random fields. As a by-product, we introduce some new results on multiple Riemann-Stieltjes integrals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_11110 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Characterization of continuous stationary fields as generalized Ornstein-Uhlenbeck fields via multi-parameter Langevin equation and multiple Riemann-Stieltjes integration Voutilainen, Marko Ilmonen, Pauliina Viitasaari, Lauri Probability 60G05, 60G60, 60G10, 60G18, 26B99 In this article, we characterize continuous stationary fields via generalized Langevin dynamics. This gives natural connections between stationary fields, stationary increment fields, self-similar fields, and generalized Langevin dynamics. Our contribution extends some recently proved similar results for stochastic processes to the case of continuous random fields. As a by-product, we introduce some new results on multiple Riemann-Stieltjes integrals. |
| title | Characterization of continuous stationary fields as generalized Ornstein-Uhlenbeck fields via multi-parameter Langevin equation and multiple Riemann-Stieltjes integration |
| topic | Probability 60G05, 60G60, 60G10, 60G18, 26B99 |
| url | https://arxiv.org/abs/2511.11110 |