We consider stochastic evolution equations in Hilbert spaces with merely measurable and locally bounded drift term B and cylindrical Wiener noise. We prove pathwise (hence strong) uniqueness in the class of global solutions. This paper extends our previous paper (Da Prato et al. in Ann Probab 41:3306–3344, 2013) which generalized Veretennikov’s fundamental result to infinite dimensions assuming boundedness of the drift term. As in Da Prato et al. (Ann Probab 41:3306–3344, 2013), pathwise uniqueness holds for a large class, but not for every initial condition. We also include an application of our result to prove existence of strong solutions when the drift B is assumed only to be measurable and bounded and grow more than linearly.
|Autori:||G. Da Prato, F. Flandoli, E. Priola , M. Röckner|
|Titolo:||Strong Uniqueness for Stochastic Evolution Equations with Unbounded Measurable Drift Term|
|Anno del prodotto:||2014|
|Digital Object Identifier (DOI):||10.1007/s10959-014-0545-0|
|Appare nelle tipologie:||1.1 Articolo in rivista|