5 research outputs found
Strong uniqueness for stochastic evolution equations with unbounded measurable drift term
We consider stochastic evolution equations in Hilbert spaces with merely
measurable and locally bounded drift term and cylindrical Wiener noise. We
prove pathwise (hence strong) uniqueness in the class of global solutions. This
paper extends our previous paper (Da Prato, Flandoli, Priola and M. Rockner,
Annals of Prob., published online in 2012) which generalized Veretennikov's
fundamental result to infinite dimensions assuming boundedness of the drift
term. As in our previous paper 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 is only measurable,
locally bounded and grows more than linearly.Comment: The paper will be published in Journal of Theoretical Probability.
arXiv admin note: text overlap with arXiv:1109.036