The Mathematics of errors / Nicolas Bouleau.

Format:

Book

Author/Creator:

Bouleau, Nicolas, author.

Language:

English

Subjects (All):

Stochastic analysis.

Error analysis (Mathematics).

Mathematical models.

Physical Description:

1 online resource (444 pages)

Place of Publication:

Springer Nature 2022

Summary:

The Mathematics of Errors presents an original, rigorous and systematic approach to the calculus of errors, targeted at both the engineer and the mathematician. Starting from Gauss's original point of view, the book begins as an introduction suitable for graduate students, leading to recent developments in stochastic analysis and Malliavin calculus, including contributions by the author. Later chapters, aimed at a more mature audience, require some familiarity with stochastic calculus and Dirichlet forms. Sensitivity analysis, in particular, plays an important role in the book. Detailed applications in a range of fields, such as engineering, robotics, statistics, financial mathematics, climate science, or quantum mechanics are discussed through concrete examples. Throughout the book, error analysis is presented in a progressive manner, motivated by examples and appealing to the reader's intuition. By formalizing the intuitive concept of error and richly illustrating its scope for application, this book provides readers with a blueprint to apply advanced mathematics in practical settings. As such, it will be of immediate interest to engineers and scientists, whilst providing mathematicians with an original presentation. Nicolas Bouleau has directed the mathematics center of the Ecole des Ponts ParisTech for more than ten years. He is known for his theory of error propagation in complex models. After a degree in engineering and architecture, he decided to pursue a career in mathematics under the influence of Laurent Schwartz. He has also written on the production of knowledge, sustainable economics and mathematical models in finance. Nicolas Bouleau is a recipient of the Prix Montyon from the French Academy of Sciences.

Contents:

Introduction Part I A la Gauss Calculations 1 The Different Approaches 2 Finite-Dimensional Examples 3 An Intuitive Introduction to Error Structures 4 Weakly and Strongly Random Errors Part II Probabilistic and Functional Models 5 Strongly Continuous Semi-Groups and Dirichlet Forms 6 Error Structures 7 Images and Products of Error Structures 8 The Gradient and the Sharp and Other Calculation Tools 9 Error Structures on Fundamental Spaces Part III The Subtleness of the Notion of Bias 10 Approximation and Bias Operators 11 Computations and Simulation Methods Part IV Error Structures in Applications 12 Statistical Identification of Error Structures 13 The Instantaneous Error Structure of a Stochastic Process 14 Models Inspired by Finance 15 Examples in Physics 16 The Principle of Arbitrary Functions and Error Structures Part V Historical Elements and Research Themes 17 Error Calculations From Gauss and Laplace 18 Extensions and Open Questions 19 Hints for Exercises Chronological Bibliography

Notes:

Includes bibliographical references and index.

Description based on print version record.

Other Format:

Print version: Bouleau, Nicolas The Mathematics of Errors

ISBN:

9783030885755