Uniqueness for stochastic evolution equations in Banach spaces

Volume 426 / 2004

Martin Ondreját Dissertationes Mathematicae 426 (2004), 1-63 MSC: Primary 60H15. DOI: 10.4064/dm426-0-1


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.


  • Martin OndrejátInstitut Élie Cartan
    Université Henri Poincaré Nancy 1
    Vandœuvre-lès-Nancy, France
    Mathematical Institute AS CR
    Žitná 25
    115 67 Praha 1, Czech Republic

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