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.

Klappentext

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.

Inhalt

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