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  • © 2021

The Mathematics of Errors

Authors:

  • Sets error calculus on rigorous mathematical foundations

  • Contains numerous worked out examples and exercices

  • Introduces the reader to recent developments and open questions in the field

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eBook USD 119.00
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  • ISBN: 978-3-030-88575-5
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Hardcover Book USD 159.99
Price excludes VAT (USA)

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Table of contents (19 chapters)

  1. Front Matter

    Pages i-xii
  2. A la Gauss Calculations

    1. Front Matter

      Pages 1-3
    2. The Different Approaches

      • Nicolas Bouleau
      Pages 5-10
    3. Finite-Dimensional Examples

      • Nicolas Bouleau
      Pages 11-22
    4. An Intuitive Introduction to Error Structures

      • Nicolas Bouleau
      Pages 23-39
    5. Weakly and Strongly Random Errors

      • Nicolas Bouleau
      Pages 41-45
  3. Probabilistic and Functional Models

    1. Front Matter

      Pages 47-49
    2. Error Structures

      • Nicolas Bouleau
      Pages 71-90
    3. Images and Products of Error Structures

      • Nicolas Bouleau
      Pages 91-107
    4. Error Structures on Fundamental Spaces

      • Nicolas Bouleau
      Pages 145-203
  4. The Subtleness of the Notion of Bias

    1. Front Matter

      Pages 205-207
    2. Approximation and Bias Operators

      • Nicolas Bouleau
      Pages 209-248
    3. Computations and Simulation Methods

      • Nicolas Bouleau
      Pages 249-279
  5. Error Structures in Applications

    1. Front Matter

      Pages 281-282
    2. Statistical Identification of Error Structures

      • Nicolas Bouleau
      Pages 283-293
    3. Models Inspired by Finance

      • Nicolas Bouleau
      Pages 311-340
    4. Examples in Physics

      • Nicolas Bouleau
      Pages 341-361

About this book

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.

Keywords

  • Ornstein-Uhlenbeck
  • error structures
  • square field operator
  • stochastic differential equation
  • variance of error
  • bias of error
  • Malliavin calculus
  • Mathematical Finance
  • Quantitative Finance

Authors and Affiliations

  • École des Ponts ParisTech, Paris, France

    Nicolas Bouleau

About the author

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.

Bibliographic Information

Buying options

eBook USD 119.00
Price excludes VAT (USA)
  • ISBN: 978-3-030-88575-5
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Hardcover Book USD 159.99
Price excludes VAT (USA)