Abrupt decorrelation for linear stochastic differential equations
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916043964809216 |
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| author | López, Sergio I. Pardo, Juan C. Pimentel, Leandro P. R. |
| author_facet | López, Sergio I. Pardo, Juan C. Pimentel, Leandro P. R. |
| contents | Understanding how a system loses memory of its initial state is a central problem in probability and statistics. In this manuscript, we introduce the notion of abrupt decorrelation, which explicitly characterises a sharp and sudden loss of correlation over time. We study this phenomenon within a class of linear stochastic differential equations (LSDEs), where explicit descriptions are available under various statistical distances. Our main focus is on the multivariate Ornstein-Uhlenbeck process, while in the one-dimensional case we extend the analysis to LSDEs with time-dependent drifts. The results highlight strong parallels with the cut-off phenomenon in Markov processes and contribute to a broader understanding of decorrelation in stochastic systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_16828 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Abrupt decorrelation for linear stochastic differential equations López, Sergio I. Pardo, Juan C. Pimentel, Leandro P. R. Probability 37A25, 60G10, 60G15, 60J60 Understanding how a system loses memory of its initial state is a central problem in probability and statistics. In this manuscript, we introduce the notion of abrupt decorrelation, which explicitly characterises a sharp and sudden loss of correlation over time. We study this phenomenon within a class of linear stochastic differential equations (LSDEs), where explicit descriptions are available under various statistical distances. Our main focus is on the multivariate Ornstein-Uhlenbeck process, while in the one-dimensional case we extend the analysis to LSDEs with time-dependent drifts. The results highlight strong parallels with the cut-off phenomenon in Markov processes and contribute to a broader understanding of decorrelation in stochastic systems. |
| title | Abrupt decorrelation for linear stochastic differential equations |
| topic | Probability 37A25, 60G10, 60G15, 60J60 |
| url | https://arxiv.org/abs/2509.16828 |