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An inverse-stochastic-control Galerkin estimator for drift potentials — arXiv:2610.04268

Source

arXiv (en)

Original

https://arxiv.org/abs/2610.04268

License (as archived)

CC0-1.0

Archived

2026-10-06T13:05:09.998Z

SHA-256 of the archived text

100e8f00660e4d80ee1ae4da61a7258a0ad95e04fe292ce769e2ab2e44c0539f

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How to cite

An inverse-stochastic-control Galerkin estimator for drift potentials — arXiv:2610.04268 — arXiv (en), https://arxiv.org/abs/2610.04268 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_1ec45fa508af (Metraipolis archive dc_1ec45fa508af, sha256 100e8f00660e4d80ee1ae4da61a7258a0ad95e04fe292ce769e2ab2e44c0539f)

@misc{dc1ec45fa508af,
  title = {An inverse-stochastic-control Galerkin estimator for drift potentials — arXiv:2610.04268},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.04268},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_1ec45fa508af; sha256 100e8f00660e4d80ee1ae4da61a7258a0ad95e04fe292ce769e2ab2e44c0539f},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.04268. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We consider the ill-posed inverse problem of recovering the drift potential of an overdamped Langevin diffusion from discrete, possibly irregular position observations. Specializing the suboptimality gap for inverse stochastic control to drift-potential recovery, we parametrize the associated value function in a finite basis. Under a basis nondegeneracy condition, the resulting Galerkin estimator is obtained from one positive-definite linear system whose entries are smooth functionals of the empirical time marginals; no transition density is required. The gap equals one half of the squared energy distance to the true potential, yielding a best-approximation identity and energy-seminorm consistency as the basis becomes complete. At a fixed basis, we separate the sample fluctuation from the time-quadrature error, thereby avoiding the Euler--Maruyama $O(\Delta t)$ drift-discretization bias. We also analyze the finite basis as regularization, give a dimension-dependent convergence rate for a concrete basis family, and bound observation-noise bias. One- and two-dimensional experiments verify the predicted sampling-interval behavior. An application to irregular animal telemetry illustrates the method on a single long trajectory.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.OC, nuovi lavori del giorno).
Categorie arXiv: Optimization and Control (math.OC) ; Statistics Theory (math.ST).
Pagina del lavoro: https://arxiv.org/abs/2610.04268 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-06T11:21:31.880Z dalla pagina https://arxiv.org/list/math.OC/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).