This book explores recent advances in uncertainty quantification for hyperbolic, kinetic, and related problems. The contributions address a range of different aspects, including: polynomial chaos expansions, perturbation methods, multi-level Monte Carlo methods, importance sampling, and moment methods. The interest in these topics is rapidly growing, as their applications have now expanded to many areas in engineering, physics, biology and the social sciences. Accordingly, the book provides the scientific community with a topical overview of the latest research efforts.

Shi Jin is a Vilas Distinguished Achievement Professor of Mathematics at the University of Wisconsin-Madison. He earned his B.S. from Peking University and his Ph.D. from the University of Arizona. His research fields include computational fluid dynamics, kinetic equations, hyperbolic conservation laws, high frequency waves, quantum dynamics, and uncertainty quantification fields in which he has published over 140 papers. He has been honored with the Feng Kang Prize in Scientific Computing and the Morningside Silver Medal of Mathematics at the Fourth International Congress of Chinese Mathematicians, and is a Fellow of both the American Mathematical Society and the Society for Industrial and Applied Mathematics (SIAM).

Lorenzo Pareschi is a Full Professor of Numerical Analysis at the Department of Mathematics and Computer Science, University of Ferrara, Italy. He received his Ph.D. in Mathematics from the University of Bologna, Italy and subsequently held visiting professor appointments at the University of Wisconsin-Madison, the University of Orleans and University of Toulouse, France, and the Imperial College, London, UK. His research interests include multiscale modeling and numerical methods for phenomena described by time dependent nonlinear partial differential equations, in particular by means of hyperbolic balance laws and kinetic equations. He is the author/editor of nine books and more than 110 papers in peer-reviewed journals.

1 The Stochastic Finite Volume Method.- 2 Uncertainty Modeling and Propagation in Linear Kinetic Equations.- 3 Numerical Methods for High-Dimensional Kinetic Equations.- 4 From Uncertainty Propagation in Transport Equations to Kinetic Polynomials.- 5 Uncertainty Quantification for Kinetic Models in Socio-Economic and Life Sciences.- 6 Uncertainty Quantification for Kinetic Equations.- 7 Monte-Carlo Finite-Volume Methods in Uncertainty Quantification for Hyperbolic Conservation Laws.