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.
@book{bwmeta1.element.bwnjournal-rm-doi-10_4064-dm426-0-1,
author = {Martin Ondrej\'at},
title = {Uniqueness for stochastic evolution equations in Banach spaces},
series = {GDML\_Books},
year = {2004},
zbl = {1053.60071},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-rm-doi-10_4064-dm426-0-1}
}
Martin Ondreját. Uniqueness for stochastic evolution equations in Banach spaces. GDML_Books (2004), http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-rm-doi-10_4064-dm426-0-1/