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Cover: 9781441918963 | Noise Theory and Application to Physics | Philippe Réfrégier | Buch
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Noise Theory and Application to Physics
From Fluctuations to Information
Taschenbuch von Philippe Réfrégier
Sprache: Englisch

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Beschreibung
I had great pleasure in reading Philippe Refregier's book on the theory of noise and its applications in physics. The main aim of the book is to present the basic ideas used to characterize these unwanted random signals that obscure information content. To this end, the author devotes a sigificant part of his book to a detailed study of the probabilistic foundations of fluctuation theory. Following a concise and accurate account of the basics of probability the­ ory, the author includes a detailed study of stochastic processes, emphasizing the idea of the correlation function, which plays a key role in many areas of physics. Physicists often assume that the noise perturbing a signal is Gaussian. This hypothesis is justified if one can consider that the noise results from the superposition of a great many independent random perturbations. It is this fact that brings the author to discuss the theory underlying the addition of random variables, accompanied by a wide range of illustrative examples. Since noise affects information, the author is naturally led to consider Shannon's information theory, which in turn brings him to the altogether fundamental idea of entropy. This chapter is completed with a study of com­ plexity according to Kolmogorov. This idea is not commonly discussed in physics and the reader will certainly appreciate the clear presentation within these pages.
I had great pleasure in reading Philippe Refregier's book on the theory of noise and its applications in physics. The main aim of the book is to present the basic ideas used to characterize these unwanted random signals that obscure information content. To this end, the author devotes a sigificant part of his book to a detailed study of the probabilistic foundations of fluctuation theory. Following a concise and accurate account of the basics of probability the­ ory, the author includes a detailed study of stochastic processes, emphasizing the idea of the correlation function, which plays a key role in many areas of physics. Physicists often assume that the noise perturbing a signal is Gaussian. This hypothesis is justified if one can consider that the noise results from the superposition of a great many independent random perturbations. It is this fact that brings the author to discuss the theory underlying the addition of random variables, accompanied by a wide range of illustrative examples. Since noise affects information, the author is naturally led to consider Shannon's information theory, which in turn brings him to the altogether fundamental idea of entropy. This chapter is completed with a study of com­ plexity according to Kolmogorov. This idea is not commonly discussed in physics and the reader will certainly appreciate the clear presentation within these pages.
Zusammenfassung
Noise in physics is related to a variety of domains, such as information theory, statistical physics, probability, stochastic processes and statistics. Noise Theory and Application to Physics provides a general background on noise theory, along with techniques to describe and extract information in the presence of fluctuations, with the goal of featuring noise in the context of its connection with other domains. Readers will gain a deep understanding of noise theory, while acquiring systematic techniques for describing and extracting noise data.
Inhaltsverzeichnis
1. The Binomial No-Arbitrage Pricing Model
1.1. One-Period Binomial Model
1.2. Multiperiod Binomial Model
1.3. Computational Considerations
1.4. Summary
1.5. Notes
1.6. Exercises 2. Probability Theory on Coin Toss Space
2.1. Finite Probability Spaces
2.2. Random Variables, Distributions, and Expectations
2.3. Conditional Expectations
2.4. Martingales
2.5. Markov Processes
2.6. Summary
2.7. Notes
2.8. Exercises 3. State Prices
3.1. Change of Measure
3.2. Radon-Nikod'ym Derivative Process
3.3. Capital Asset Pricing Model
3.4. Summary
3.5. Notes
3.6. Exercises 4. American Derivative Securities
4.1. Introduction
4.2. Non-Path-Dependent American Derivatives
4.3. Stopping Times
4.4. General American Derivatives
4.5. American Call Options
4.6. Summary
4.7. Notes
4.8. Exercises 5. Random Walk
5.1. Introduction
5.2. First Passage Times
5.3. Reflection Principle
5.4. Perpetual American Put: An Example
5.5. Summary
5.6. Notes
5.7. Exercises 6. Interest-Rate-Dependent Assets
6.1. Introduction
6.2. Binomial Model for Interest Rates
6.3. Fixed-Income Derivatives
6.4. Forward Measures
6.5. Futures
6.6. Summary
6.7. Notes
6.8. Exercises
Proof of Fundamental Properties of Conditional Expectations
References
Index
Details
Erscheinungsjahr: 2011
Fachbereich: Theoretische Physik
Genre: Physik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Advanced Texts in Physics
Inhalt: xiii
288 S.
80 s/w Illustr.
ISBN-13: 9781441918963
ISBN-10: 1441918965
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Réfrégier, Philippe
Auflage: Softcover reprint of the original 1st ed. 2004
Hersteller: Springer New York
Springer US, New York, N.Y.
Advanced Texts in Physics
Maße: 235 x 155 x 17 mm
Von/Mit: Philippe Réfrégier
Erscheinungsdatum: 12.12.2011
Gewicht: 0,464 kg
Artikel-ID: 107253306
Zusammenfassung
Noise in physics is related to a variety of domains, such as information theory, statistical physics, probability, stochastic processes and statistics. Noise Theory and Application to Physics provides a general background on noise theory, along with techniques to describe and extract information in the presence of fluctuations, with the goal of featuring noise in the context of its connection with other domains. Readers will gain a deep understanding of noise theory, while acquiring systematic techniques for describing and extracting noise data.
Inhaltsverzeichnis
1. The Binomial No-Arbitrage Pricing Model
1.1. One-Period Binomial Model
1.2. Multiperiod Binomial Model
1.3. Computational Considerations
1.4. Summary
1.5. Notes
1.6. Exercises 2. Probability Theory on Coin Toss Space
2.1. Finite Probability Spaces
2.2. Random Variables, Distributions, and Expectations
2.3. Conditional Expectations
2.4. Martingales
2.5. Markov Processes
2.6. Summary
2.7. Notes
2.8. Exercises 3. State Prices
3.1. Change of Measure
3.2. Radon-Nikod'ym Derivative Process
3.3. Capital Asset Pricing Model
3.4. Summary
3.5. Notes
3.6. Exercises 4. American Derivative Securities
4.1. Introduction
4.2. Non-Path-Dependent American Derivatives
4.3. Stopping Times
4.4. General American Derivatives
4.5. American Call Options
4.6. Summary
4.7. Notes
4.8. Exercises 5. Random Walk
5.1. Introduction
5.2. First Passage Times
5.3. Reflection Principle
5.4. Perpetual American Put: An Example
5.5. Summary
5.6. Notes
5.7. Exercises 6. Interest-Rate-Dependent Assets
6.1. Introduction
6.2. Binomial Model for Interest Rates
6.3. Fixed-Income Derivatives
6.4. Forward Measures
6.5. Futures
6.6. Summary
6.7. Notes
6.8. Exercises
Proof of Fundamental Properties of Conditional Expectations
References
Index
Details
Erscheinungsjahr: 2011
Fachbereich: Theoretische Physik
Genre: Physik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Advanced Texts in Physics
Inhalt: xiii
288 S.
80 s/w Illustr.
ISBN-13: 9781441918963
ISBN-10: 1441918965
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Réfrégier, Philippe
Auflage: Softcover reprint of the original 1st ed. 2004
Hersteller: Springer New York
Springer US, New York, N.Y.
Advanced Texts in Physics
Maße: 235 x 155 x 17 mm
Von/Mit: Philippe Réfrégier
Erscheinungsdatum: 12.12.2011
Gewicht: 0,464 kg
Artikel-ID: 107253306
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