Fundamental Notions in Stochastic Modeling of Uncertainties and their Propagation in Computational Models.- Elements of Probability Theory.- Markov Process and Stochastic Differential Equation.- MCMC Methods for Generating Realizations and for Estimating the Mathematical Expectation of Nonlinear Mappings of Random Vectors.- Fundamental Probabilistic Tools for Stochastic Modeling of Uncertainties.- Brief Overview of Stochastic Solvers for the Propagation of Uncertainties.- Fundamental Tools for Statistical Inverse Problems.- Uncertainty Quantification in Computational Structural Dynamics and Vibroacoustics.- Robust Analysis with Respect to the Uncertainties for Analysis, Updating, Optimization, and Design.- Random Fields and Uncertainty Quantification in Solid Mechanics of Continuum Media.
Christian Soize is professor at Universite Paris-Est Marne-la-Valee. His research interests include stochastic modeling of uncertainties in computational mechanics, their propagation and their quantification.
"The book under review serves as an excellent reference for the uncertainty analysis community. ... the author has included an extensive bibliography in the end of the book that will be very useful to the interested reader. ... the book is an excellent reference for advanced users and practitioners of UQ and is strongly recommended." (Tujin Sahai, Mathematical Reviews, September, 2018)