STATISTICAL APPROACH TO DYNAMICAL INVERSE PROBLEMS

Authors
CHOW PL KHASMINSKII RZ
Citation
Pl. Chow et Rz. Khasminskii, STATISTICAL APPROACH TO DYNAMICAL INVERSE PROBLEMS, Communications in Mathematical Physics, 189(2), 1997, pp. 521-531
Citations number
16
Categorie Soggetti
Mathematical Method, Physical Science","Physycs, Mathematical
Journal title
Communications in Mathematical Physics → ACNP
ISSN journal
00103616
Volume
189
Issue
2
Year of publication
1997
Pages
521 - 531
Database
ISI
SICI code
0010-3616(1997)189:2<521:SATDIP>2.0.ZU;2-7
Abstract
Based on nonparametric estimation ideas, a statistical approach to the dynamical inverse problem for some n(th) order nonlinear differential equations is introduced. It is proved that the real-time filter type of estimators converge respectively, as the data noise tends to zero, to the unknown force function and its derivatives at an optimal rate i n the minimax sense.