PreprintCC BY-NC-ND 4.0arXiv
On statistical inference for non-linear dynamical systems evolving in their global attractor
Abstract
We consider a periodic scalar reaction-diffusion system over a two-dimensional domain under natural conditions on the reaction function and with initial condition θ. We show that on the global attractor 𝒜 of the resulting dynamical system (uθ(t):t>0), a reverse Poincaré inequality holds true, and that as a consequence the map θ↦ uθ(t) satisfies an L2(Om)-Lipschitz stability estimate on 𝒜 for any t>0 fixed. We then show that statistical recovery of an initial condition θ in the attractor 𝒜, as well as prediction of the states uθ, is possible from discrete measurements of the system at parametric 1/√N convergence rates.
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BibTeX
@misc{konen2026statistical,
title = {{On statistical inference for non-linear dynamical systems evolving in their global attractor}},
author = {Dimitri Konen and Richard Nickl},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2606.06018},
eprint = {2606.06018},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.06018},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - On statistical inference for non-linear dynamical systems evolving in their global attractor
AU - Dimitri Konen
AU - Richard Nickl
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2606.06018
UR - https://arxiv.org/abs/2606.06018
AB - We consider a periodic scalar reaction-diffusion system over a two-dimensional domain under natural conditions on the reaction function and with initial condition θ. We show that on the global attractor 𝒜 of the resulting dynamical system (u_θ(t):t>0), a reverse Poincaré inequality holds true, and that as a consequence the map θ↦ u_θ(t) satisfies an L^2(Om)-Lipschitz stability estimate on 𝒜 for any t>0 fixed. We then show that statistical recovery of an initial condition θ in the attractor 𝒜, as well as prediction of the states u_θ, is possible from discrete measurements of the system at parametric 1/√N convergence rates.
ER -