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)
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