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| Main Authors: | , |
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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2603.17142 |
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| _version_ | 1866910057591996416 |
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| author | Recke, Cecilie Olesen Hansen, Niels Richard |
| author_facet | Recke, Cecilie Olesen Hansen, Niels Richard |
| contents | Cross-sectional observations from a dynamical system can be modeled via steady-state distributions of Markov processes. The major challenge is then to determine whether the process parameters can be identified and estimated from the steady-state distributions. We study this problem for continuous Lyapunov models that arise as steady-state distributions of the solution to a multivariate stochastic differential equation, whose linear drift matrix is parametrized by a directed graph. We derive equations for the cumulant tensors of any order for this distribution, which generalize the well-known covariance Lyapunov equation. Under a non-Gaussianity assumption we prove generic identifiability of the drift matrix for any connected graph using the equations for the higher-order cumulants. Based on the identifiability result, we propose a new semiparametric estimator of the drift matrix, and we derive its asymptotic distribution. A simulation study demonstrates the asymptotic validity of the estimator but shows that it is only accurate for relatively large sample sizes, illustrating the hardness of the unconstrained estimation problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_17142 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Identifiability and Estimation in Continuous Lyapunov Models Recke, Cecilie Olesen Hansen, Niels Richard Statistics Theory Cross-sectional observations from a dynamical system can be modeled via steady-state distributions of Markov processes. The major challenge is then to determine whether the process parameters can be identified and estimated from the steady-state distributions. We study this problem for continuous Lyapunov models that arise as steady-state distributions of the solution to a multivariate stochastic differential equation, whose linear drift matrix is parametrized by a directed graph. We derive equations for the cumulant tensors of any order for this distribution, which generalize the well-known covariance Lyapunov equation. Under a non-Gaussianity assumption we prove generic identifiability of the drift matrix for any connected graph using the equations for the higher-order cumulants. Based on the identifiability result, we propose a new semiparametric estimator of the drift matrix, and we derive its asymptotic distribution. A simulation study demonstrates the asymptotic validity of the estimator but shows that it is only accurate for relatively large sample sizes, illustrating the hardness of the unconstrained estimation problem. |
| title | Identifiability and Estimation in Continuous Lyapunov Models |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2603.17142 |