Guaranteed Estimation Problems in the Theory of Linear Ordinary Differential Equations with Uncertain Data.

• Author: Nakonechnyi, Oleksandr.
• Place / Publishing House: Aalborg : : River Publishers,, 2021.; Ã2021.
• Year of Publication: 2021
• Edition: 1st ed.
• Language: English
• Physical Description: 1 online resource (234 pages)

This monograph is devoted to the construction of optimal estimates of values of linear functionals on solutions to Cauchy and two-point boundary value problems for systems of linear first-order ordinary differential equations, from indirect observations which are linear transformations of the same solutions perturbed by additive random noises.

Table of Contents

Front Cover -- Guaranteed Estimation Problems in the Theory of Linear Ordinary Differential Equations with Uncertain Data -- Contents -- Preface -- Introduction -- 1 Guaranteed Estimates of Solutions and Right-Hand Sides of the Cauchy Problem Under Incomplete Data -- 1.1 Preliminaries and Auxiliary Results -- 1.2 Statement of the Estimation Problem -- 1.3 Minimax Estimation of Functionals From Solutions of the Cauchy Problem -- 1.4 1-Optimal Estimates of Unknown Solution of the Cauchy Problem -- 1.5 Representations of Guaranteed Estimates of Functionals -- 1.6 Minimax Estimation of the Right-Hand Sides of Equalities that Enter -- 1.7 Guaranteed Estimation of Solutions to the Cauchy Problem -- 1.8 Guaranteed Predictive Estimation of Solutions to the Cauchy Problem -- 2 Guaranteed Estimation of Unknown Solutions and Right-Hand Sides of First Order Linear Systems of Periodic ODEs -- 2.1 Guaranteed Estimation of Solutions of First Order Linear Systems -- 2.2 Guaranteed Recovery of Unknown Right-Hand Sides -- 2.3 Guaranteed a Posteriori Estimation of Unknown Right-Hand Sides -- 3 Guaranteed Estimation of Solutions of Boundary Value Problems for Linear Ordinary Differential Equations with Decomposed Boundary Data -- 3.1 Preliminaries and Auxiliary Results -- 3.2 Statement of the Minimax Estimation Problem and Its Reduction -- 3.3 Representations for Minimax Estimates of Functionals from Solutions -- 3.4 Minimax Estimates of Solutions Subject to Incomplete Restrictions -- 3.5 Elimination Technique in Minimax Estimation Problems -- 3.6 Minimax Estimation of the Solutions to the Boundary Value Problems -- 3.7 Results of Numerical Experiments -- 4 Guaranteed Estimation of Parameters of Boundary Value Problems for Linear Ordinary Differential Equations with General Boundary Data -- 4.1 Auxiliary Results.

4.2 Statement of the Estimation Problem of Solutions -- 4.3 Representations for Minimax Estimates of the Values of Functionals -- 4.4 Minimax Estimation of Functionals from Right-Hand Sides -- 4.5 Minimax Estimation of Functionals from Solutions -- 4.6 Auxiliary Results -- 4.7 Statement of Estimation Problem -- 4.8 Theorems on the General form of Minimax Estimates -- 4.9 Estimation Problems of Functionals from Unknown Data -- References -- Index -- About the Authors -- Back Cover.