Linear stochastic systems with constant coefficients: a statistical approach
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin u.a.
Springer
1982
|
| Series: | Lecture notes in control and information sciences
45 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 309 S. graph. Darst. |
| ISBN: | 3540120904 0387120904 |
Staff View
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| 245 | 1 | 0 | |a Linear stochastic systems with constant coefficients |b a statistical approach |c M. Arató |
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Record in the Search Index
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| adam_text | CONTENTS
Chapter 1
Case Studies, Problems and Their Statistical Investigation 1
1.1. Introductionary Remarks 1
1.2. The Brownian Motion 6
1.3. The Torsion Pendulum and Electrical Circuits 13
1.4. The Chandler Wobble 27
1.4.1. The Rotation of the Earth 27
1.4.2. The Mathematical Description and Statistical
Investigation 33
1.5. System Descrition 44
1.6. Measurement Analysis in Computer Systems 52
1.6.1. Measurement of Performance 52
1.6.2. Round off Errors in Solutions of Ordinary
Differential Equations 60
1.7. Sunspot Activity 70
1.8. Kalman Filtering with Explicite Solutions (Sigftal Plus
Noise Case) 79
Chapter 2
Elementary Gaussian Processes 95
2.1. Processes with Discrete Time 95
2.1.1. Main Theorems 95
2.1.2. Structure of Degenerate and Deterministic Processes 100
2.1.3. Spectral Representation of Processes, Autoregressive
and Moving Average Type Processes 103
2.2. Processes with Continuous Time 118
2.2.1. Main Theorems 118
2.2.2. Stationary Gaussian Processes with Rational Spectral
Density Functions 127
2.3. Density Functions and Sufficient Statistics 137
2.3.1. The Discrete Time Case 137
2.3.2. Some Auxiliary Theorems 144
2.3.3. The Radon Nikodym Derivatives with Respect
to the Wiener Measure 151
2.3.4. Unobservable Components 159
VIII
Chapter 3
The Maximum Likelihood Estimators and their Distributions
in the One Dimensional Case 169
3.1. The Basic Principles of Statistical Estimation Theory 169
3.2. The Unknown Mean 176
3.3. The Unknown X 177
3.4. Two Unknown Parameters 185
3.5. The Discrete Time Case 193
3.5.1. Single Parameters 193
3.5.2. Distribution of the Derivatives of Likelihood
Function 198
3.5.3. Asymptotic Distribution of Maximum Likelihood
Estimates 207
3.5.4. Results Obtained for Discrete Analogues of the
Continuous time Case 210
3.6. The Moments of Estimators and Asymptotic Theory 214
3.6.1. Sequential Estimation 218
Chapter 4
Multi Dimensional Processes 221
4.1. The Complex Process 221
4.2. Construction of Confidence Intervals for the Parameter X 225
4.3. Estimation of the Period 236
4.4. The Uknown Mean 239
4.4.1. The Complex Process 239
4.4.2. Linear Regression 240
4.4.3. Correct Estimates 242
4.4.4. Pitman s Estimates 245
4.4.5. Admissible Estimates 247
4.4.6. Minimax Weigths in Trend Detection 250
4.5. Real Roots and Other Special Cases 253
4.6. Multi Dimensional Case, Asymptotic Theory 258
Appendix A
Linear Differential Equations with Constant Coefficients 263
1. Preliminary Definitions and Notations, Matrices 263
IX
2. Linear Systems with Constant Coefficients 268
Appendix B
Probability Bakcground 272
1. Gaussian Systems 272
2. Some Basic Concepts in Probability Theory 280
General Bibliography
Books 288
References 294
Authors1 index 308
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| id | DE-604.BV000229511 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:10:46Z |
| institution | BVB |
| isbn | 3540120904 0387120904 |
| language | English |
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| physical | IX, 309 S. graph. Darst. |
| psigel | TUB-nveb |
| publishDate | 1982 |
| publishDateSearch | 1982 |
| publishDateSort | 1982 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in control and information sciences |
| series2 | Lecture notes in control and information sciences |
| spelling | Arató, Mátyás 1931- Verfasser (DE-588)103871849X aut Linear stochastic systems with constant coefficients a statistical approach M. Arató Berlin u.a. Springer 1982 IX, 309 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in control and information sciences 45 Stochastic differential equations Stochastic systems Lineares stochastisches System (DE-588)4167737-7 gnd rswk-swf Stochastisches System (DE-588)4057635-8 gnd rswk-swf Lineares stochastisches System (DE-588)4167737-7 s DE-604 Stochastisches System (DE-588)4057635-8 s Lecture notes in control and information sciences 45 (DE-604)BV005848579 45 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000137470&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Arató, Mátyás 1931- Linear stochastic systems with constant coefficients a statistical approach Lecture notes in control and information sciences Stochastic differential equations Stochastic systems Lineares stochastisches System (DE-588)4167737-7 gnd Stochastisches System (DE-588)4057635-8 gnd |
| subject_GND | (DE-588)4167737-7 (DE-588)4057635-8 |
| title | Linear stochastic systems with constant coefficients a statistical approach |
| title_auth | Linear stochastic systems with constant coefficients a statistical approach |
| title_exact_search | Linear stochastic systems with constant coefficients a statistical approach |
| title_full | Linear stochastic systems with constant coefficients a statistical approach M. Arató |
| title_fullStr | Linear stochastic systems with constant coefficients a statistical approach M. Arató |
| title_full_unstemmed | Linear stochastic systems with constant coefficients a statistical approach M. Arató |
| title_short | Linear stochastic systems with constant coefficients |
| title_sort | linear stochastic systems with constant coefficients a statistical approach |
| title_sub | a statistical approach |
| topic | Stochastic differential equations Stochastic systems Lineares stochastisches System (DE-588)4167737-7 gnd Stochastisches System (DE-588)4057635-8 gnd |
| topic_facet | Stochastic differential equations Stochastic systems Lineares stochastisches System Stochastisches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000137470&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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