Statistical approach to dynamical inverse problems

被引：5

作者：

Chow, PL

Khasminskii, RZ

机构：

[1] Department of Mathematics, Wayne State University, Detroit

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 1997年 / 189卷 / 02期

关键词：

Differential Equation; Inverse Problem; Statistical Approach; Nonlinear Differential Equation; Optimal Rate;

D O I：

10.1007/s002200050215

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

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 in the minimax sense.

引用

页码：521 / 531

页数：11

共 16 条

[1]

Banks H. T., 1989, ESTIMATION TECHNIQUE

[2]

DONOHO DL, 1991, NONLINEAR SOLUTION L

[3]

Ermakov M S., 1989, Probl. Pereda. Inf, V25, P28

[4] WELL-POSED STOCHASTIC EXTENSIONS OF ILL-POSED LINEAR PROBLEMS [J].

FRANKLIN, JN .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1970, 31 (03) :682-&

[5]

GOLUBEV GK, 1985, PROBLEMS INFORMATION, V21, P36

[6]

HADARNARD J, 1932, PROBLEME CAUCHY EQUA

[7]

IBRAGIMOV IA, 1980, THEOR PROBAB APPL+, V25, P703, DOI 10.1137/1125086

[8]

IBRAGIMOV IA, 1981, STATISTICAL ESTIMATI

[9]

Ivanov V. K., 1963, MAT SBORNIK, V61, P211

[10]

JOHNSTONE IM, 1991, J COMPLEXITY, V1, P1

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