Non-selection of Lagrangian trajectories in the zero-noise limit for a class of stochastic regularizations

Lucio Galeati, Filippo Giovagnini, Massimo Sorella

We prove the lack of selection in the zero-noise limit for solutions to SDEs driven by a divergence-free, Hölder continuous vector field with exponent $\hat{I}\pm \in (0,1)$, arbitrarily cl…