Mathematical models of information and stochastic systems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton, Fla. [u.a.]
CRC Press / Taylor & Francis Group
2008
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturangaben |
| Beschreibung: | VIII, 364 S. Ill., graph. Darst. |
| ISBN: | 1420058835 9781420058833 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804142704666345472 |
|---|---|
| adam_text | Titel: Mathematical models of information and stochastic systems
Autor: Kornreich, Philipp
Jahr: 2008
Contents
Chapter 1 Introduction..........................................................................................1
1.1 Historical Development and Aspects of Probability Theory..........................1
1.2 Discussion of the Material in This Text..........................................................5
References..................................................................................................................7
Chapter 2 Events and Density of Events...............................................................9
2.1 General Probability Concepts.........................................................................9
2.2 Probabilities of Continuous Sets of Events...................................................16
2.3 Discrete Events Having the Same Probability..............................................18
2.4 Digression of Factorials and the F Function.................................................26
2.5 Continuous Sets of Events Having the Same Probability,
Density of States...........................................................................................29
Problems..................................................................................................................33
Chapter 3 Joint, Conditional, and Total Probabilities.........................................41
3.1 Conditional Probabilities...............................................................................41
3.2 Dependent, Independent, and Exclusive Events............................................44
3.3 Total Probability and Bayes Theorem of Discrete Events...........................44
3.4 Markov Processes.........................................................................................47
3.5 Joint, Conditional, and Total Probabilities and Bayes Theorem
of Continuous Events....................................................................................51
Problems..................................................................................................................55
Chapter 4 Random Variables and Functions of Random Variables....................61
4.1 Concept of a Random Variable and Functions of a Random Variable.........61
4.2 Discrete Distribution Functions....................................................................62
4.3 Discrete Distribution Functions for More than One Value
of a Random Variable with the Same Probability.........................................64
4.4 Continuous Distribution and Density Functions...........................................65
4.5 Continuous Distribution Functions for More than One Value
of a Random Variable with the Same Probability.........................................68
4.6 Discrete Distribution Functions of Multiple Random Variables...................69
4.7 Continuous Distribution Functions of Multiple Random Variables..............72
4.8 Phase Space: A Special Case of Multiple Random Variables.......................76
Problems..................................................................................................................77
vi Mathematical Models of Information and Stochastic Systems
Chapter 5 Conditional Distribution Functions and a Special Case:
The Sum of Two Random Variables..................................................83
5.1 Discrete Conditional Distribution Functions................................................83
5.2 Continuous Conditional Distribution Functions...........................................84
5.3 A Special Case: The Sum of Two Statistically Independent Discrete
Random Variables.........................................................................................86
5.4 A Special Case: The Sum of Two Statistically Independent Continuous
Random Variables.........................................................................................91
Problems..................................................................................................................95
Chapter 6 Average Values, Moments, and Correlations of Random
Variables and of Functions of Random Variables..............................99
6.1 The Most Likely Value of a Random Variable.............................................99
6.2 The Average Value of a Discrete Random Variable and of a Function
of a Discrete Random Variable.....................................................................99
6.3 An Often-Used Special Case......................................................................100
6.4 The Probabilistic Mathematical Model of Discrete Quantum
Mechanics...................................................................................................101
6.5 The Average Value of a Continuous Random Variable and of a
Function of a Continuous Random Variable...............................................120
6.6 The Probabilistic Model of Continuous Quantum Mechanics...................121
6.7 Moments of Random Variables...................................................................128
6.8 Conditional Average Value of a Random Variable and of a Function
of a Random Variable..................................................................................131
6.9 Central Moments.........................................................................................132
6.10 Variance and Standard Deviation...............................................................132
6.11 Correlations of Two Random Variables and of Functions of Random
Variables......................................................................................................135
6.12 A Special Case: The Average Value of e-Jkx................................................140
References..............................................................................................................142
Problems................................................................................................................142
Chapter 7 Randomness and Average Randomness...........................................149
7.1 The Concept of Randomness of Discrete Events........................................149
7.2 The Concept of Randomness of Continuous Events...................................152
7.3 The Average Randomness of Discrete Events............................................154
7.4 The Average Randomness of Continuous Random Variables....................158
7.5 The Average Randomness of Random Variables with Values That
Have the Same Probability..........................................................................161
7.6 The Entropy of Real Physical Systems and a Very Large Number............164
7.7 TheCepstrum..............................................................................................166
7.8 Stochastic Temperature and the Legendre Transform................................166
7.9 Other Stochastic Potentials and the Noise Figure.......................................172
References..............................................................................................................175
Problems................................................................................................................175
Contents vü
Chapter 8 Most Random Systems.....................................................................181
8.1 Methods for Determining Probabilities......................................................181
8.2 Determining Probabilities Based on What Is Known about a System.......187
8.3 The Poisson Probability and One of Its Applications.................................199
8.4 Continuous Most Random Systems............................................................204
8.5 Properties of Gaussian Stochastic Systems.................................................208
8.6 Important Examples of Stochastic Physical Systems..................................221
8.7 The Limit of Zero and Very Large Temperatures.......................................233
References..............................................................................................................236
Problems................................................................................................................236
Chapter 9 Information.......................................................................................241
9.1 Information Concepts..................................................................................241
9.2 Information in Genes..................................................................................251
9.3 Information Transmission of Discrete Systems..........................................253
9.4 Information Transmission of Continuous or Analog Systems....................258
9.5 The Maximum Information and Optimum Transmission Rates
of Discrete Systems.....................................................................................260
9.6 The Maximum Information and Optimum Transmission Rates
of Continuous or Analog Systems...............................................................263
9.7 The Bit Error Rate.......................................................................................269
References..............................................................................................................272
Problems................................................................................................................272
Chapter 10 Random Processes............................................................................279
10.1 Random Processes......................................................................................279
10.2 Random Walk and the Famous Case of Scent Molecules Emerging
from a Perfume Bottle.................................................................................280
10.3 The Simple Stochastic Oscillator and Clocks.............................................284
10.4 Correlation Functions of Random Processes..............................................292
10.5 Stationarity of Random Processes..............................................................292
10.6 The Time Average and Ergodicity of Random Processes...........................296
10.7 Partially Coherent Light Rays as Random Processes.................................297
10.8 Stochastic Aspects of Transitions between States......................................301
10.9 Cantor Sets as Random Processes..............................................................307
References..............................................................................................................308
Problems................................................................................................................309
Chapter 11 Spectral Densities.............................................................................315
11.1 Stochastic Power.........................................................................................315
11.2 The Power Spectrum and Cross-Power Spectrum......................................318
11.3 The Effects of Filters on the Autocorrelation Function and the
Power Spectral Density...............................................................................321
vüi Mathematical Models of Information and Stochastic Systems
11.4 The Bandwidth of the Power Spectrum......................................................323
Problems................................................................................................................325
Chapter 12 Data Analysis...................................................................................329
12.1 Least Square Differences............................................................................329
12.2 The Special Case of Linear Regression......................................................331
12.3 Other Examples...........................................................................................333
Problems................................................................................................................333
Chapter 13 Chaotic Systems...............................................................................337
13.1 Fractals........................................................................................................337
13.2 Mandelbrot Sets..........................................................................................341
13.3 Difference Equations..................................................................................343
13.4 The Hénon Difference Equation.................................................................345
13.5 Single-Particle Single-Well Potential..........................................................348
References..............................................................................................................351
Index......................................................................................................................353
|
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| dewey-hundreds | 000 - Computer science, information, general works |
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| dewey-sort | 13.76015118 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik Mathematik |
| format | Book |
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| indexdate | 2024-07-09T22:36:00Z |
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| isbn | 1420058835 9781420058833 |
| language | English |
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| physical | VIII, 364 S. Ill., graph. Darst. |
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| publisher | CRC Press / Taylor & Francis Group |
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| spelling | Kornreich, Philipp Verfasser (DE-588)138142114 aut Mathematical models of information and stochastic systems Philipp Kornreich Boca Raton, Fla. [u.a.] CRC Press / Taylor & Francis Group 2008 VIII, 364 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturangaben Stochastisches System (DE-588)4057635-8 gnd rswk-swf Informationssystem (DE-588)4072806-7 gnd rswk-swf Stochastik (DE-588)4121729-9 gnd rswk-swf Mathematische Modellierung (DE-588)7651795-0 gnd rswk-swf Stochastik (DE-588)4121729-9 s DE-604 Stochastisches System (DE-588)4057635-8 s Informationssystem (DE-588)4072806-7 s Mathematische Modellierung (DE-588)7651795-0 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020135505&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kornreich, Philipp Mathematical models of information and stochastic systems Stochastisches System (DE-588)4057635-8 gnd Informationssystem (DE-588)4072806-7 gnd Stochastik (DE-588)4121729-9 gnd Mathematische Modellierung (DE-588)7651795-0 gnd |
| subject_GND | (DE-588)4057635-8 (DE-588)4072806-7 (DE-588)4121729-9 (DE-588)7651795-0 |
| title | Mathematical models of information and stochastic systems |
| title_auth | Mathematical models of information and stochastic systems |
| title_exact_search | Mathematical models of information and stochastic systems |
| title_full | Mathematical models of information and stochastic systems Philipp Kornreich |
| title_fullStr | Mathematical models of information and stochastic systems Philipp Kornreich |
| title_full_unstemmed | Mathematical models of information and stochastic systems Philipp Kornreich |
| title_short | Mathematical models of information and stochastic systems |
| title_sort | mathematical models of information and stochastic systems |
| topic | Stochastisches System (DE-588)4057635-8 gnd Informationssystem (DE-588)4072806-7 gnd Stochastik (DE-588)4121729-9 gnd Mathematische Modellierung (DE-588)7651795-0 gnd |
| topic_facet | Stochastisches System Informationssystem Stochastik Mathematische Modellierung |
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