Théorie des erreurs

Book in French — English title: Theory of Errors

460 pages. Black & white.

The classical methods of error calculation, devised at the beginning of the 19^th century by the mathematicians Laplace and Gauss to estimate the accuracy of astronomical calculations, have long been of great service to physicists and engineers. But they are ill-suited to the calculations carried out today in increasingly complex models, particularly those involving randomness.

In structural analysis, control engineering, signal processing, statistics, financial mathematics, satellite guidance, climate forecasting and quantum mechanics, their indiscriminate application precludes proper control of precision and tolerances. It had therefore become necessary to develop new methods built on rigorous mathematical foundations. Many researchers, among them Nicolas Bouleau, have worked on this since the 1990s, and their work is now sufficiently mature to be set out in the form of a textbook intended for students and engineers alike. These new tools are suited to the celebrated Itō calculus and to the random processes that can be constructed from Brownian motion — it was with the same ideas that Paul Malliavin succeeded in improving Hörmander’s theorem on elliptic equations.

The theory is presented very gradually, and the book is accessible to third-year undergraduates and first-year engineering school students. But the applications it offers in a wide range of fields also make it a useful book across the whole spectrum of the applied sciences.