Noise Theory and Application to Physics: From Fluctuations to Information

ISBN-13: 9781441918963 / Angielski / Miękka / 2011 / 288 str.

Philippe Refregier

Opis

This is a unique approach to noise theory and its application to physical measurements that will find its place among the graduate course books. In a very systematic way, the foundations are laid and applied in a way that the book will also be useful to those not focusing on optics. Exercises and solutions help students to deepen their knowledge.

Recenzje

From the reviews:

"Philippe Réfrégier's book is an introduction to the fundamental principles of randomness that can be encountered in a physicist's everyday life. ... Réfrégier's book is a good textbook for physics graduate students and researchers who want to go a little deeper into probability theory ... . I would also recommend it to mathematicians who want to get a different point of view on probability theory. Students will undoubtedly profit from a variety of exercises that come with ... solutions." (Achim Klenke, Zentralblatt MATH, Vol. 1092 (18), 2006)

"The book provides a good presentation of the statistical basis for theories of noise in physics. ... Noise theory and application to physics provides a precise description of the theoretical background and practical tools for noise and fluctuation analyses. It will thus be of great interest to undergraduate or postgraduate students and researchers in physics and the engineering sciences." (Stefan Adams, Mathematical Reviews, Issue 2006 e)

Spis treści

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

O autorze

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.

Blurb

In many situations, physical quantities are perturbed or evolve in a not fully predictable way. We then speak about noise or fluctuations and we are generally faced to different questions such as: What are the correct physical models to describe them? What are the most practical mathematical tools to deal with them? How can relevant information be extracted in the presence of noise?

Noise theory and application to physics provides a precise description of the theoretical background and practical tools for noise and fluctuation analyses. It not only introduces basic mathematical descriptions and properties of noise and fluctuations but also discusses the physical origin of different noise models and presents some statistical methods which optimize measurements in the presence of such fluctuations.

Noise theory and application to physics investigates a number of ideas about noise and fluctuations in a single book in relation with probability and stochastic processes, information theory, statistical physics and statistical inference. The different notions are illustrated with many application examples from physics and engineering science and problems with solutions allow the reader to both check his understanding and to deepen some aspects.

Indeed, the main objective of Noise theory and application to physics is to be a practical guide for the reader for going from fluctuation to information. It will thus be of great interest to undergraduate or postgraduate students and researchers in physics and engineering sciences.