Noise theory and application to physics: from fluctuations to information
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German English |
| Published: |
New York [u.a.]
Springer
2004
|
| Series: | Advanced texts in physics
Physics and astronomy online library |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 288 S. graph. Darst. |
| ISBN: | 0387201548 |
Staff View
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Record in the Search Index
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|---|---|
| adam_text | PHILIPPE REFREGIER NOISE THEORY AND APPLICATION TO PHYSICS FROM
FLUCTUATIONS TO INFORMATION WITH 80 FIGURES SPRINGER CONTENTS * /
INTRODUCTION 1 RANDOM VARIABLES 5 2.1 RANDOM EVENTS AND PROBABILITY 6
2.2 RANDOM VARIABLES 7 2.3 MEANS AND MOMENTS 10 2.4 MEDIAN AND MODE OF A
PROBABILITY DISTRIBUTION 12 2.5 JOINT RANDOM VARIABLES 13 2.6 COVARIANCE
16 2.7 CHANGE OF VARIABLES 18 2.8 STOCHASTIC VECTORS 19 EXERCISES 22
FLUCTUATIONS AND COVARIANCE 25 3.1 STOCHASTIC PROCESSES 25 3.2
STATIONARITY AND ERGODICITY 28 3.3 ERGODICITY IN STATISTICAL PHYSICS 32
3.4 GENERALIZATION TO STOCHASTIC FIELDS 34 3.5 RANDOM SEQUENCES AND
CYCLOSTATIONARITY 35 3.6 ERGODIC AND STATIONARY CASES 40 3.7 APPLICATION
TO OPTICAL COHERENCE 41 3.8 FIELDS AND PARTIAL DIFFERENTIAL EQUATIONS 42
3.9 POWER SPECTRAL DENSITY A . 44 3.10 FILTERS AND FLUCTUATIONS 46 3.11
APPLICATION TO OPTICAL IMAGING 50 3.12 GREEN FUNCTIONS AND FLUCTUATIONS
52 3.13 STOCHASTIC VECTOR FIELDS 56 3.14 APPLICATION TO THE POLARIZATION
OF LIGHT 57 3.15 ERGODICITY AND POLARIZATION OF LIGHT 61 3.16 APPENDIX:
WIENER-KHINCHINE THEOREM 64 EXERCISES 66 XII CONTENTS 4 LIMIT THEOREMS
AND FLUCTUATIONS 71 4.1 SUM OF RANDOM VARIABLES 71 4.2 CHARACTERISTIC
FUNCTION 74 4.3 CENTRAL LIMIT THEOREM 76 4.4 GAUSSIAN NOISE AND STABLE
PROBABILITY LAWS 80 4.5 A SIMPLE MODEL OF SPECKLE 81 4.6 RANDOM WALKS .
89 4.7 APPLICATION TO DIFFUSION 92 4.8 RANDOM WALKS AND SPACE DIMENSIONS
97 4.9 RARE EVENTS AND PARTICLE NOISE 100 4.10 LOW FLUX SPECKLE 102
EXERCISES 104 5 INFORMATION AND FLUCTUATIONS 109 5.1 SHANNON INFORMATION
109 5.2 ENTROPY ILL 5.3 KOLMOGOROV COMPLEXITY 114 5.4 INFORMATION AND
STOCHASTIC PROCESSES 117 5.5 MAXIMUM ENTROPY PRINCIPLE 119 5.6 ENTROPY
OF CONTINUOUS DISTRIBUTIONS 122 5.7 ENTROPY, PROPAGATION AND DIFFUSION
124 5.8 MULTIDIMENSIONAL GAUSSIAN CASE 128 5.9 KULLBACK-LEIBLER MEASURE
: 130 5.10 APPENDIX: LAGRANGE MULTIPLIERS 133 EXERCISES 134 6
THERMODYNAMIC FLUCTUATIONS 137 6.1 GIBBS STATISTICS 137 6.2 FREE ENERGY
141 6.3 CONNECTION WITH THERMODYNAMICS 142 6.4 COVARIANCE OF
FLUCTUATIONS 143 6.5 A SIMPLE EXAMPLE 146 6.6 FLUCTUATION-DISSIPATION
THEOREM 149 6.7 NOISE AT THE TERMINALS OF AN RC CIRCUIT 153 6.8 PHASE
TRANSITIONS 158 6.9 CRITICAL FLUCTUATIONS , 161 EXERCISES 163 7
STATISTICAL ESTIMATION 167 7.1 THE EXAMPLE OF POISSON NOISE 167 7.2 THE
LANGUAGE OF STATISTICS 169 7.3 CHARACTERIZING AN ESTIMATOR 169 7.4
MAXIMUM LIKELIHOOD ESTIMATOR , 174 7.5 CRAMER-RAO BOUND IN THE SCALAR
CASE 177 7.6 EXPONENTIAL FAMILY 179 CONTENTS XIII 7.7 EXAMPLE
APPLICATIONS 181 7.8 CRAMER-RAO BOUND IN THE VECTORIAL CASE 182 7.9
LIKELIHOOD AND THE EXPONENTIAL FAMILY 183 7.10 EXAMPLES IN THE
EXPONENTIAL FAMILY 186 7.10.1 ESTIMATING THE PARAMETER IN THE POISSON
DISTRIBUTION 187 7.10.2 ..ESTIMATING THE MEAN OF THE GAMMA DISTRIBUTION
187 7.10.3 ESTIMATING THE MEAN OF THE GAUSSIAN DISTRIBUTION 188 7.10.4
ESTIMATING THE VARIANCE OF THE GAUSSIAN DISTRIBUTION .. 189 7.10.5
ESTIMATING THE MEAN OF THE WEIBULL DISTRIBUTION 190 7.11 ROBUSTNESS OF
ESTIMATORS 192 7.12 APPENDIX: SCALAR CRAMER-RAO BOUND 196 7.13 APPENDIX:
EFFICIENT STATISTICS 199 7.14 APPENDIX: VECTORIAL CRAMER-RAO BOUND 200
EXERCISES 205 8 EXAMPLES OF ESTIMATION IN PHYSICS 209 8.1 MEASUREMENT OF
OPTICAL FLUX 209 8.2 MEASUREMENT ACCURACY IN THE PRESENCE OF GAUSSIAN
NOISE .... 212 8.3 ESTIMATING A DETECTION EFFICIENCY 217 8.4^ ESTIMATING
THE COVARIANCE MATRIX 219 8.5 APPLICATION TO COHERENCY MATRICES 221 8.6
MAKING ESTIMATES IN THE PRESENCE OF SPECKLE 224 8.7
FLUCTUATION-DISSIPATION AND ESTIMATION 225 EXERCISES 227 9 SOLUTIONS TO
EXERCISES 231 9.1 CHAPTER TWO. RANDOM VARIABLES 231 9.2 CHAPTER THREE.
FLUCTUATIONS AND COVARIANCE 235 9.3 CHAPTER FOUR. LIMIT THEOREMS AND
FLUCTUATIONS 243 9.4 CHAPTER FIVE. INFORMATION AND FLUCTUATIONS 250 9.5
CHAPTER SIX. STATISTICAL PHYSICS 259 9.6 CHAPTER SEVEN. STATISTICAL
ESTIMATION 266 9.7 CHAPTER EIGHT. EXAMPLES OF ESTIMATION IN PHYSICS 271
REFERENCES 285 INDEX 287
|
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| author | Réfrégier, Philippe |
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| dewey-full | 530.15/92 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.15/92 |
| dewey-search | 530.15/92 |
| dewey-sort | 3530.15 292 |
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| discipline | Maschinenbau / Maschinenwesen Physik |
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| indexdate | 2024-07-09T19:58:11Z |
| institution | BVB |
| isbn | 0387201548 |
| language | German English |
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| physical | XIII, 288 S. graph. Darst. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Springer |
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| series2 | Advanced texts in physics Physics and astronomy online library |
| spelling | Réfrégier, Philippe Verfasser aut Théorie du bruit et applications en physique Noise theory and application to physics from fluctuations to information Philippe Réfrégier New York [u.a.] Springer 2004 XIII, 288 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Advanced texts in physics Physics and astronomy online library Entropy (Information theory) Fluctuations (Physics) Fluktuation Physik (DE-588)4130671-5 gnd rswk-swf Rauschen (DE-588)4048606-0 gnd rswk-swf Rauschen (DE-588)4048606-0 s DE-604 Fluktuation Physik (DE-588)4130671-5 s HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012812101&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Réfrégier, Philippe Noise theory and application to physics from fluctuations to information Entropy (Information theory) Fluctuations (Physics) Fluktuation Physik (DE-588)4130671-5 gnd Rauschen (DE-588)4048606-0 gnd |
| subject_GND | (DE-588)4130671-5 (DE-588)4048606-0 |
| title | Noise theory and application to physics from fluctuations to information |
| title_alt | Théorie du bruit et applications en physique |
| title_auth | Noise theory and application to physics from fluctuations to information |
| title_exact_search | Noise theory and application to physics from fluctuations to information |
| title_full | Noise theory and application to physics from fluctuations to information Philippe Réfrégier |
| title_fullStr | Noise theory and application to physics from fluctuations to information Philippe Réfrégier |
| title_full_unstemmed | Noise theory and application to physics from fluctuations to information Philippe Réfrégier |
| title_short | Noise theory and application to physics |
| title_sort | noise theory and application to physics from fluctuations to information |
| title_sub | from fluctuations to information |
| topic | Entropy (Information theory) Fluctuations (Physics) Fluktuation Physik (DE-588)4130671-5 gnd Rauschen (DE-588)4048606-0 gnd |
| topic_facet | Entropy (Information theory) Fluctuations (Physics) Fluktuation Physik Rauschen |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012812101&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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