Uniqueness for stochastic evolution equations in Banach spaces. (English) Zbl 1053.60071

Ondreját, Martin

Diss. Math. 426, 1-63 (2004).

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)