An introduction to vector stochastic processes:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Huntington, NY
Krieger
1980
|
| Series: | Applied mathematics series: Mathematics for engineering and science
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VII, 214 S. |
| ISBN: | 0882758551 |
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Record in the Search Index
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| adam_text | Table of Contents
Preface v
Chapter I. Linear Vector Spaces and Matrices 1
1. Introduction 2
2. Differentiation with respect to vectors and matrices 5
3. Hessians 9
4. A differential equation in Banach spaces 11
5. Sequences of matrices 17
6. Stochastic vectors 23
7. Integration of random vectors 26
8. Some properties of norrns 32
Chapter II. Vector Linear Least Squares 39
1. The Gauss Markov theorem 39
2. Recursive form of the Markov estimate 44
3. The Kalman approach 48
4. Properties of least squares and Markov estimates 57
5. Maximum likelihood estimators 64
Chapter III. Vector Stochastic Processes 71
1. Stationary processes 72
2. Processes with orthogonal increments 77
3. Stochastic integrals 82
iii
iv TABLE OF CONTENTS
4. Spectral representation 87
5. White noise integrals 90
6. Brownian motion 99
Chapter IV. Vector Linear Differential Equations 107
1. Existence and uniqueness 108
2. The Wronskian matrix 110
3. The adjoint operator 115
4. Higher order equations 118
5. Variation of solution with initial conditions 123
6. Constant coefficient differential equations 124
7. Matric differential equations 125
8. Stochastic differential equations 132
9. Spectral matrix relations 136
10. The Kalman filter 141
11. A comparison of least squares and Kalman method 146
Chapter V. Distributions of Random Vectors 153
1. Gaussian random vectors 154
2. The multivariate Rayleigh distribution 159
3. The multivariate uniform distribution 166
4. The multivariate lognormal distribution 171
5. Distributions of homogeneous random vectors 176
6. Functions of quadratic forms 193
7. Vector Gauss Markov processes 202
References 209
Index 211
|
| any_adam_object | 1 |
| author | Miller, Kenneth S. |
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| indexdate | 2024-07-09T17:23:01Z |
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| isbn | 0882758551 |
| language | English |
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| physical | VII, 214 S. |
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| publisher | Krieger |
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| series2 | Applied mathematics series: Mathematics for engineering and science |
| spelling | Miller, Kenneth S. Verfasser (DE-588)1159045585 aut An introduction to vector stochastic processes by Kenneth S. Miller Huntington, NY Krieger 1980 VII, 214 S. txt rdacontent n rdamedia nc rdacarrier Applied mathematics series: Mathematics for engineering and science Stochastic processes Vector spaces HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005718512&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Miller, Kenneth S. An introduction to vector stochastic processes Stochastic processes Vector spaces |
| title | An introduction to vector stochastic processes |
| title_auth | An introduction to vector stochastic processes |
| title_exact_search | An introduction to vector stochastic processes |
| title_full | An introduction to vector stochastic processes by Kenneth S. Miller |
| title_fullStr | An introduction to vector stochastic processes by Kenneth S. Miller |
| title_full_unstemmed | An introduction to vector stochastic processes by Kenneth S. Miller |
| title_short | An introduction to vector stochastic processes |
| title_sort | an introduction to vector stochastic processes |
| topic | Stochastic processes Vector spaces |
| topic_facet | Stochastic processes Vector spaces |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005718512&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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