Stochastic Equations in Infinite Dimensions

Giuseppe Da Prato, Jerzy Zabczyk

• Publisher: Cambridge University Press
• Year: 2014
• Print ISBN: 9781107055841
• eBook ISBN: 9781139899598
• Edition: 2
• Topic: Mathematics
• Subtopic: Differential Equations
• Index: Mathematics

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 differential equations.

Table of contents

• Cover
• Half title
• Series
• Title
• Copyright
• Contents
• Preface
• Introduction: motivating examples
• Part I Foundations
• Part II Existence and uniqueness
• Part III Properties of solutions
• Appendix A: Linear deterministic equations
• Appendix B: Some results on control theory
• Appendix C: Nuclear and Hilbert–Schmidt operators
• Appendix D: Dissipative mappings
• Bibliography
• Index