Point processes and coincidences: contributions to the theory : with applications to statistical optics and optical communication
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Weitere Verfasser: | , |
| Format: | Abschlussarbeit Buch |
| Sprache: | English French |
| Veröffentlicht: |
Nächst Neuendorf
Walter Warmuth Verlag
2017
|
| Schriftenreihe: | Classical Lectures
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Beschreibung: | 305 Seiten 21 cm, 397 g |
| ISBN: | 9783944311036 3944311035 |
Internformat
MARC
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| 240 | 1 | 0 | |a Macchi, Odile |
| 245 | 1 | 0 | |a Point processes and coincidences |b contributions to the theory : with applications to statistical optics and optical communication |c Odile Macchi ; augmented with a scholion by Suren Poghosyan and Hans Zessin ; English translation: Hans Zessin |
| 264 | 1 | |a Nächst Neuendorf |b Walter Warmuth Verlag |c 2017 | |
| 300 | |a 305 Seiten |c 21 cm, 397 g | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Classical Lectures | |
| 502 | |b Dissertation |c Université de Paris Sud |d 1972 |g unter dem Titel: Processus ponctuels et coincidences | ||
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Datensatz im Suchindex
| _version_ | 1804178418794758144 |
|---|---|
| adam_text | CONTENTS
1 INTRODUCTION 15
1 SOME GENERAL RESULTS 25
2 POINT PROCESSES AND COINCIDENCES 27
2.1 IN TRO D U C TIO N
.............................................................................................27
2.2 REGULAR PROCESSES AND COINCIDENCE D E N S IT IE S
..........................
28
2.2.1 ASSUMPTIONS FOR ORDERLY PROCESSES
............................................
28
2.2.2 COINCIDENCE AND EXCLUSION PROBABILITIES
...................................
30
2.3 SHOT NOISE P RO C E S S E S
...........................................................................34
2.3.1
DEFINITION.........................................................................................34
2.3.2 CHARACTERISTIC FUNCTION OF ORDER Q
............................................
35
2.3.3 JOINT DISTRIBUTION OF COUNTING V A RIA B LE S
...................................
37
2.4 EXCLUSION D E N S ITIE S
..........................
41
2.4.1 EXCLUSION (PROBABILITY)
DENSITIES.................................................41
2.4.2 DISTANCES BETWEEN INSTANTS AND IMPULSES
...............................
42
2.4.3 INTERVALS BETWEEN NEIGHBOURING IM PULSES
...............................
43
2.4.4 SURVIVALTIME AND
LIFETIME..............................................................
44
2.5 S TA TIO N A R ITY
.............................................................................................
45
2.6 OPERATIONS ON POINT P RO C E S S E S
..........................................................47
2.6.1 SUPERPOSITION
................................................................................
47
2.6.2 RANDOM
THINNING............................................................................49
2.7 E X A M P LE S
..................................................................................................49
2.7.1 THE POISSON P RO C E S S
................................................................... 49
2.7.2 DETECTION OF A MONO-MODE FIELD WITH N PHOTONS
......................
51
2.A ADDITIONAL P RO O FS
....................................................................................54
LAWS OF REGULAR POINT PROCESSES 57
3.1 THE SPACE OF RE A LIZ A TIO N S
...................................................................57
3.1.1 SYMMETRIC SETS IN
3N.................................................................. 58
3.2 E V E N T S
......................................................................................................
58
3.2.1 THE COUNTING A LG E B RA
................................................................... 59
3.2.2 DISTRIBUTIONS OF P ELEM ENTS
..........................................................
62
3.3 PROBABILITY L A W S
....................................................................................
67
3.3.1 EXCLUSION
PROBABILITIES...................................................................
68
3.3.2 SYMMETRY OF L A W S
.......................................................................
69
3.3.3 COINCIDENCE P RO B A B ILITIE S
..........................................................
71
3.3.4 PROBABILITIES OF CYLINDERS IN AND
....................................74
3.3.5 MOMENTS AND FACTORIAL MOMENTS
.................................................
75
3.4 REGULAR POINT
PROCESSES.......................................................................
80
3.4.1 DENSITIES OF EXCLUSION P RO B A B ILITIE S
........................................
80
3.4.2 COINCIDENCE PROBABILITY D E N S ITIE S
.............................................82
3.4.3 CONSTRUCTION OF POINT PROCESSES
.................................................
67
3.5 A-FINITE POINT P RO C E S S E S
.......................................................................
91
3.5.1 EXCLUSION
PROBABILITIES...................................................................
92
3.5.2 COINCIDENCE
DENSITIES...................................................................
93
3.6 CHARACTERISTIC FU N C TIO N A LS
...................................................................96
II POINT PROCESS MODELS 101
4 COX PROCESSES AND PHOTOELECTRONS 103
4.1 IN TRO D U C TIO N
...........................................................................................
103
4.2 DETECTION OF AN OPTICAL F I E L D
............................................................
104
4.3 THE COX P RO C E S S
..................................................................................
106
4.3.1
DEFINITION.......................................................................................106
4.3.2 CHARACTERISTIC AND GENERATING FU N C TIO N
.................................
108
4.3.3 EXCLUSION PROBABILITIES
................................................................
110
4.3.4
STATIONARITY..................................................................................
112
4.3.5 SUPERPOSITION AND
THINNING........................................................112
4.4 THERM AL L I G H T
.......................................................................................113
4.4.1
INTRODUCTION..................................................................................
113
4.4.2 THE GENERATING FUNCTION OF IM PU LSES
......................................
114
4.4.3 THE METHOD OF COINCIDENCES
...................................................
115
4.4.4 EXCLUSION
PROBABILITIES.................................................................116
4.4.5 EXAMPLE: THERMAL LIGHT WITH LORENTZ-SPECTRUM
....................
119
4.5 THE DOUBLY STOCHASTIC POISSON P R O C E S S
......................................
122
4.5.1 JOINT
LAWS.......................................................................................122
4.5.2
COINCIDENCES..............................................................................123
4.6 THE GAUSS-POISSON P RO C E S S
............................................................
125
4.6.1 M O TIV A TIO N
..................................................................................
125
4.6.2 THE CHARACTERISTIC FUN CTIO N AL
...................................................
125
4.6.3
COINCIDENCES..............................................................................129
4.6.4 EXCLUSION PROBABILITIES AND AN EXISTENCE THEOREM. . . . 130
4.6.5 THE STATIONARY
CASE.....................................................................
132
4.6.6 AN
EXAMPLE..................................................................................
133
4.6.7 PROOF OF THEOREM 4 . 4
................................................................
134
4 .A PROOF OF FORMULA ( 4 . 6 6 )
.....................................................................135
5 RENEWAL PROCESSES 139
5.1 D E FIN ITIO N
................................................................................................139
5.2 EXCLUSION PROBABILITIES
.........................................................................
140
5.3 JOINT COUNTING LA W S
..............................................................................141
6 FERMIONS IN A CHAOTIC STATE 145
6.1 IN TRO D U C TIO N
............................................................................................145
6.2 CHARACTERIZATION OF FERM
IONS.............................................................146
6.2.1
GENERALITIES...................................................................................146
6.2.2 GENERATING FUNCTION OF THE COUNTING V A R IA B LE S
....................
147
6.2.3 NECESSARY AND SUFFICIENT CONDITIONS FOR G TO BE A GENER
ATING FU N CTIO N
..............................................................................
150
6.2.4 A BASIC
THEOREM..........................................................................155
6.3 FERMIONS IN A CHAOTIC STATE: PHYSICAL POINT OF VIEW .... 162
6.3.1
INTRODUCTION...................................................................................162
6.3.2 THE M O D E S
...................................................................................162
6.3.3 DENSITY MATRICES. EMISSION AND DETECTION PROCESSES . .163
6.3.4 D
ISCUSSION...................................................................................165
6.4 AN ANALOGY BETWEEN CHAOTIC BEAM S
OF FERMIONS AND OF B O S O N S
................................................................. 168
6.5 AN E X A M P LE
............................................................................................170
6.5.1
INTRODUCTION...................................................................................170
6.5.2 IS A GENERALIZED RENEWAL PROCESS
......................................
170
6.5.3 LORENTZIAN ASSUMPTIONS
............................................................
172
III OPTICAL COMMUNICATIONS 175
7 WEAK OPTICAL SIGNALS 177
7.1 IN TRO D U C TIO N
............................................................................................177
7.2 ESTIMATION OF A MODULATED OPTICAL S IG N A L
......................................
178
7.2.1 THE P R O B LE M
..............................................................................
178
7.2.2 GENERAL R E S U LT S
..........................................................................179
7.2.3 THE CASE OF WEAK N O IS E
.............................................................182
7.2.4 AN EXAM
PLE...................................................................................184
7.3 ESTIMATION OF THE INTENSITY OF THERM AL L I G H T
..................................
188
7.4 LINEAR ES TIM A TIO N
...................................................................................
193
7.4.1 INTERNAL NOISE OF THE D ETECTO
R....................................................194
7.4.2 NOISE FROM PARASITICAL RADIATION
...............................................
196
7.5 DETECTION P RO B LE M S
..............................................................................199
7.5.1 THERMAL NOISE OF THE
DETECTOR.................................................200
7.5.2 PARASITICAL ENVIRONMENTAL RADIATION
..........................................
203
7.5.3 FINAL REM ARKS
...................................
205
7.6 C O N C LU S IO N S
...........................................................................................206
7 .A SOM E GENERAL PROPERTIES OF THE ESTIMATORS
....................................
207
7.A.1 EXPECTATION OF
AQ{TN}
................................................................
207
7.A.2 VARIANCE OF
AQ{TN)
.........................................................................208
7.A.3 PROOF OF FORMULA (7.19)
............................................................209
7.B THE R E S O LV E N T
.....................................................................................
210
IV LATER MATHEMATICAL DEVELOPMENTS 215
8 QUANTUM-CLASSICAL PROCESSES 217
8.1 IN TRO D U C TIO N
...........................................................................................218
8.1.1 SOME MATHEMATICAL T O O L S
.......................................................
223
8.2 A GENERAL CONSTRUCTION S C H E M E
.......................................................
225
8
.
2.1
NEHRING*S REPRESENTATION OF 3
L
...............................................227
8.3 A SPECIAL CLASS OF FUNCTIONALS L
.......................................................
229
8.3.1 GLOBAL ASSUMPTIONS ON THE
POTENTIALS......................................234
8.3.2 INFINITELY EXTENDED
PROCESSES...................................................237
8.3.3 EXPLICIT CONDITIONS FOR THE P O TE N TIA LS
......................................239
8.4 THE CLUSTER E Q U A T IO N
.........................................................................
240
8.4.1 A GENERAL PRINCIPLE IMPLYING A COX STRUCTURE
........................
242
8.5 FACTORIAL MOMENT M E A S U R E S
............................................................244
8.6 A REPRESENTATION OF THE MODIFIED LAPLACE TRANSFORM .... 246
9 QUANTUM PROCESSES 247
9.1 CONSTRUCTION OF QUANTUM
PROCESSES...............................................247
9.1.1 A CONSTRUCTION METHOD INDUCING QUANTUM INTERACTIONS . . 249
9.2 IMMANANTAL P R O C E S S E S
.....................................................................250
9.3 COX P RO C E S S E S
......................................................................................
253
9.4 SUPPORT P RO P E R TIE S
..............................................................................254
9.5 GIBBSIAN C H A RA C TE
R..............................................................................
255
9.6 INVARIANCE PROPERTIES AND LAWS OF LARGE N U M B E R S
....................
256
9 .7 MIXING OF QUANTUM P R O C E S S E S
........................................................259
9.8 A CENTRAL LIMIT THEOREM FOR QUANTUM P RO C E S S E S
.........................262
10 EXAMPLES OF QUANTUM PROCESSES 265
10.1 QUANTUM COX P R O C E S S E S
.................................................................267
10.1.1 THERMAL LIGHT. THE PHOTON PROCESS
..........................................
267
10.2 QUANTUM POLYA P RO
CESSES.................................................................269
10.2.1 PE IS A PAPANGELOU P RO C E S S
...................................................
270
10.3 IDEAL BOSONS AND F E R M IO N S
............................................................
272
10.3.1 LAWS OF LARGE NUMBERS AND CENTRAL LIMIT THEOREMS. . . .273
10.3.2 CLUSTERING REPRESENTATION OF 5+
...............................................
274
10.4 QUANTUM RENEWAL P RO CESSES
............................................................
275
10.5 GINIBRE P R O C E S S E S
..............................................................................
276
10.5.1 THE EXPONENTIAL KERNEL IS A QUANTUM INTERACTION . . . .276
10.5.2 C O N STRU CTIO N
..............................................................................
278
10.5.3 GIBBSIAN AND COXIAN CH A RA C TE
R............................................... 279
10.5.4 ASYMPTOTIC
BEHAVIOUR.................................................................279
11 PRESSURE OF QUANTUM SYSTEMS 283
11.1 THE P RO B LE M
............................................................................................283
11.1.1 A
DECOMPOSITION..........................................................................284
11.1.2 THE SECOND TERM
..........................................................................285
11.2 E X A M P LE S
................................................................................................286
11.2.1 POLYA
PROCESSES..........................................................................286
11.2.2 GINIBRE P RO C E S S E S
.....................................................................
286
11.2.3 IDEAL BOSONS AND FERMIONS IN THE COMPLEX PLANE .... 238
BIBLIOGRAPHY 291
|
| any_adam_object | 1 |
| author | Macchi, Odile 1943- |
| author2 | Rafler, Mathias Zessin, Hans |
| author2_role | edt trl |
| author2_variant | m r mr h z hz |
| author_GND | (DE-588)1136310541 (DE-588)1155326121 (DE-588)1136330453 (DE-588)1136343083 |
| author_facet | Macchi, Odile 1943- Rafler, Mathias Zessin, Hans |
| author_role | aut |
| author_sort | Macchi, Odile 1943- |
| author_variant | o m om |
| building | Verbundindex |
| bvnumber | BV044880799 |
| classification_rvk | SK 820 |
| ctrlnum | (OCoLC)1031923366 (DE-599)DNB1133503438 |
| dewey-full | 519.23 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.23 |
| dewey-search | 519.23 |
| dewey-sort | 3519.23 |
| dewey-tens | 510 - Mathematics |
| discipline | Physik Mathematik |
| format | Thesis Book |
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| institution | BVB |
| institution_GND | (DE-588)1067142398 |
| isbn | 9783944311036 3944311035 |
| language | English French |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030275023 |
| oclc_num | 1031923366 |
| open_access_boolean | |
| owner | DE-384 |
| owner_facet | DE-384 |
| physical | 305 Seiten 21 cm, 397 g |
| publishDate | 2017 |
| publishDateSearch | 2017 |
| publishDateSort | 2017 |
| publisher | Walter Warmuth Verlag |
| record_format | marc |
| series2 | Classical Lectures |
| spelling | Macchi, Odile 1943- Verfasser (DE-588)1136310541 aut Macchi, Odile Point processes and coincidences contributions to the theory : with applications to statistical optics and optical communication Odile Macchi ; augmented with a scholion by Suren Poghosyan and Hans Zessin ; English translation: Hans Zessin Nächst Neuendorf Walter Warmuth Verlag 2017 305 Seiten 21 cm, 397 g txt rdacontent n rdamedia nc rdacarrier Classical Lectures Dissertation Université de Paris Sud 1972 unter dem Titel: Processus ponctuels et coincidences Quantenoptik (DE-588)4047990-0 gnd rswk-swf Punktprozess (DE-588)4138173-7 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Punktprozess (DE-588)4138173-7 s Quantenoptik (DE-588)4047990-0 s DE-604 Rafler, Mathias (DE-588)1155326121 edt Zessin, Hans (DE-588)1136330453 trl Poghosyan, Suren (DE-588)1136343083 oth Dr. Walter Warmuth (Firma) (DE-588)1067142398 pbl B:DE-101 application/pdf http://d-nb.info/1133503438/04 Inhaltsverzeichnis DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030275023&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Macchi, Odile 1943- Point processes and coincidences contributions to the theory : with applications to statistical optics and optical communication Quantenoptik (DE-588)4047990-0 gnd Punktprozess (DE-588)4138173-7 gnd |
| subject_GND | (DE-588)4047990-0 (DE-588)4138173-7 (DE-588)4113937-9 |
| title | Point processes and coincidences contributions to the theory : with applications to statistical optics and optical communication |
| title_alt | Macchi, Odile |
| title_auth | Point processes and coincidences contributions to the theory : with applications to statistical optics and optical communication |
| title_exact_search | Point processes and coincidences contributions to the theory : with applications to statistical optics and optical communication |
| title_full | Point processes and coincidences contributions to the theory : with applications to statistical optics and optical communication Odile Macchi ; augmented with a scholion by Suren Poghosyan and Hans Zessin ; English translation: Hans Zessin |
| title_fullStr | Point processes and coincidences contributions to the theory : with applications to statistical optics and optical communication Odile Macchi ; augmented with a scholion by Suren Poghosyan and Hans Zessin ; English translation: Hans Zessin |
| title_full_unstemmed | Point processes and coincidences contributions to the theory : with applications to statistical optics and optical communication Odile Macchi ; augmented with a scholion by Suren Poghosyan and Hans Zessin ; English translation: Hans Zessin |
| title_short | Point processes and coincidences |
| title_sort | point processes and coincidences contributions to the theory with applications to statistical optics and optical communication |
| title_sub | contributions to the theory : with applications to statistical optics and optical communication |
| topic | Quantenoptik (DE-588)4047990-0 gnd Punktprozess (DE-588)4138173-7 gnd |
| topic_facet | Quantenoptik Punktprozess Hochschulschrift |
| url | http://d-nb.info/1133503438/04 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030275023&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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