The mathematics of errors / Nicolas Bouleau.
Bouleau, Nicolas, author.
2022
QA275
Available Online

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Title The mathematics of errors / Nicolas Bouleau.
Author Bouleau, Nicolas, author.
Uniform Title Théorie des erreurs. English
ISBN 9783030885755 (electronic bk.)
3030885755 (electronic bk.)
9783030885748
3030885747
DOI https://doi.org/10.1007/978-3-030-88575-5
Published Cham, Switzerland : Springer, 2022.
Language English
Description 1 online resource (1 volume) : illustrations (black and white).
Item Number 10.1007/978-3-030-88575-5 doi
Call Number QA275
Dewey Decimal Classification 511/.43
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 readers 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.
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Source of Description Description based on print version record.
Available in Other Form Mathematics of errors.
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I. Error computations a la Gauss
1. The different approaches
2. Finite dimensional examples
3. An intuitive introduction to error structures
4. Weakly and strongly random errors
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
III. The subtleness of the notion of bias
10. Approximation and bias operators
11. Computations and simulation methods
IV. Error structures and its applications
12. Statistical identification of error structures
13. The instantaneous structure of a stochastic process
14. Models inspired by finance
15. Examples in Physics
16. The principle of arbitrary functions and error structures
V. Historical elements and research themes
17. Error calculations from Gauss and Laplace
18. Extensions and open questions
Hints for exercises
Pedagogical References
Chronological Bibliography.

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