Optimal parameter estimation for linear SPDEs from multiple measurements
Altmeyer R, Tiepner A, Wahl M (2022)
arXiv:2211.02496.
Preprint | Englisch
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Autor*in
Altmeyer, Randolf;
Tiepner, Anton;
Wahl, MartinUniBi
Einrichtung
Abstract / Bemerkung
The coefficients in a general second order linear stochastic partial
differential equation (SPDE) are estimated from multiple spatially localised
measurements. Assuming that the spatial resolution tends to zero and the number
of measurements is non-decreasing, the rate of convergence for each coefficient
depends on the order of the parametrised differential operator and is faster
for higher order coefficients. Based on an explicit analysis of the reproducing
kernel Hilbert space of a general stochastic evolution equation, a Gaussian
lower bound scheme is introduced. As a result, minimax optimality of the rates
as well as sufficient and necessary conditions for consistent estimation are
established.
Erscheinungsjahr
2022
Zeitschriftentitel
arXiv:2211.02496
Page URI
https://pub.uni-bielefeld.de/record/2969766
Zitieren
Altmeyer R, Tiepner A, Wahl M. Optimal parameter estimation for linear SPDEs from multiple measurements. arXiv:2211.02496. 2022.
Altmeyer, R., Tiepner, A., & Wahl, M. (2022). Optimal parameter estimation for linear SPDEs from multiple measurements. arXiv:2211.02496
Altmeyer, Randolf, Tiepner, Anton, and Wahl, Martin. 2022. “Optimal parameter estimation for linear SPDEs from multiple measurements”. arXiv:2211.02496.
Altmeyer, R., Tiepner, A., and Wahl, M. (2022). Optimal parameter estimation for linear SPDEs from multiple measurements. arXiv:2211.02496.
Altmeyer, R., Tiepner, A., & Wahl, M., 2022. Optimal parameter estimation for linear SPDEs from multiple measurements. arXiv:2211.02496.
R. Altmeyer, A. Tiepner, and M. Wahl, “Optimal parameter estimation for linear SPDEs from multiple measurements”, arXiv:2211.02496, 2022.
Altmeyer, R., Tiepner, A., Wahl, M.: Optimal parameter estimation for linear SPDEs from multiple measurements. arXiv:2211.02496. (2022).
Altmeyer, Randolf, Tiepner, Anton, and Wahl, Martin. “Optimal parameter estimation for linear SPDEs from multiple measurements”. arXiv:2211.02496 (2022).