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.

Review of the first edition:‘The exposition is excellent and readable throughout, and should help bring the theory to a wider audience.'

Daniel L. Ocone Source: Stochastics and Stochastic Reports

Review of the first edition:‘… a welcome contribution to the rather new area of infinite dimensional stochastic evolution equations, which is far from being complete, so it should provide both a useful background and motivation for further research.'

Yuri Kifer Source: The Annals of Probability

Review of the first edition:‘… an excellent book which covers a large part of stochastic evolution equations with clear proofs and a very interesting analysis of their properties … In my opinion this book will become an indispensable tool for everybody working on stochastic evolution equations and related areas.'

P. Kotelenez - American Mathematical Society