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Uniqueness for stochastic evolution equations in Banach spaces. (English) Zbl 1053.60071
Summary: Different types of uniqueness (e.g. pathwise uniqueness, uniqueness in law, joint uniqueness in law) and existence (e.g. strong solution, martingale solution) for stochastic evolution equations driven by a Wiener process are studied and compared. We show a sufficient condition for a joint distribution of a process and a Wiener process to be a solution of a given SPDE. Equivalences between different concepts of solution are shown. An alternative approach to the construction of the stochastic integral in 2-smooth Banach spaces is included as well as Burkholder’s inequality, stochastic Fubini’s theorem and the Girsanov theorem.

MSC:
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
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