Now in its second edition, this book gives a systematic and self-contained presentation of basic results on stochastic evolution equations in infinite dimensional, typically Hilbert and Banach, spaces. In the first part the authors give a self-contained exposition of the basic properties of probability measure on separable Banach and Hilbert spaces, as required later; they assume a reasonable background in probability theory and finite dimensional stochastic processes. The second part is devoted to the existence and uniqueness of solutions of a general stochastic evolution equation, and the third concerns the qualitative properties of those solutions. Appendices gather together background results from analysis that are otherwise hard to find under one roof. This revised edition includes two brand new chapters surveying recent developments in the area and an even more comprehensive bibliography, making this book an essential and up-to-date resource for all those working in stochastic di
Based on well-known lectures given at Scuola Normale Superiore in Pisa, this book introduces analysis in a separable Hilbert space of infinite dimension. It starts from the definition of Gaussian meas
Lectures: J. Chazarain, A. Piriou: Problemes mixtes hyperboliques: Premiere partie: Les problemes mixtes hyperboliques verifiant 1a condition de Lopatinski uniforme; Deuxieme partie: Propagation et re
Second order linear parabolic and elliptic equations arise frequently in mathematics and other disciplines. For example parabolic equations are to be found in statistical mechanics and solid state theory, their infinite dimensional counterparts are important in fluid mechanics, mathematical finance and population biology, whereas nonlinear parabolic equations arise in control theory. Here the authors present a state of the art treatment of the subject from a new perspective. The main tools used are probability measures in Hilbert and Banach spaces and stochastic evolution equations. There is then a discussion of how the results in the book can be applied to control theory. This area is developing very rapidly and there are numerous notes and references that point the reader to more specialised results not covered in the book. Coverage of some essential background material will help make the book self-contained and increase its appeal to those entering the subject.
This volume presents an introductory course on differential stochastic equations and Malliavin calculus.The material of the book has grown from a series of courses delivered at the Scuola Normale Supe
This book introduces differential stochastic equations and Malliavin calculus. The revised and expanded third edition offers corrections and improvements and a new section covering the differentiabili
Analyzes developments in the study of quantum random fields, control theory, white noise, and fluid dynamics. This title presents conditions for nontrivial and well-defined scattering, Gaussian noise
Focusing on stochastic porous media equations, this book places an emphasis on existence theorems, asymptotic behavior and ergodic properties of the associated transition semigroup. Stochastic perturb
This book consists of five introductory contributions by leading mathematicians on the functional analytic treatment of evolution equations. In particular the contributions deal with Markov semigroups
