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The aim of this book is to give a systematic and self-contained presentation of basic results on stochastic evolution equations in infinite dimensional, typically Hilbert and Banach, spaces. These are a generalization of stochastic differential equations as introduced by Itô and Gikham that occur, for instance, when describing random phenomena that crop up in science and engineering, as well as in the study of differential equations. The book is divided into three parts. In the first 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. The book ends with a comprehensive bibliography that will contribute to the book's value for all working in stochastic differential equations.

Stochastic partial differential equations. --- Banach spaces, Stochastic differential equations in --- Hilbert spaces, Stochastic differential equations in --- SPDE (Differential equations) --- Stochastic differential equations in Banach spaces --- Stochastic differential equations in Hilbert spaces --- Differential equations, Partial

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Geometry [Differential ] --- Géométrie différentielle --- Inverse problems (Differential equations) --- Inversieproblemen (Differentiaalvergelijkingen) --- Meetkunde [Differentiaal] --- Problèmes inverses (Equations différentielles) --- Spectra (Wiskunde) --- Spectral theory (Mathematics) --- Spectre (Mathematiques) --- 514.84 --- Geometry, Differential --- Functional analysis --- Hilbert space --- Measure theory --- Transformations (Mathematics) --- Differential equations --- Differential geometry --- Geometric methods in quantum mechanics and in the theory of elementary particles --- 514.84 Geometric methods in quantum mechanics and in the theory of elementary particles --- Geometry, Differential. --- Differential equations, Partial --- Équations aux dérivées partielles --- Problèmes inverses --- Géometrie différentielle --- Differential equations, Partial. --- Équations aux dérivées partielles. --- Géometrie différentielle --- Problèmes inverses --- Theorie spectrale