Uniqueness for stochastic evolution equations in Banach spaces
Tom 426 / 2004
Dissertationes Mathematicae 426 (2004), 1-63
MSC: Primary 60H15.
DOI: 10.4064/dm426-0-1
Streszczenie
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.
