We revisit the zero-noise Peano selection problem for Lévy-driven stochastic differential equation considered in [Pilipenko and Proske, Statist. Probab. Lett., 132:62–73, 2018] and show that the selection phenomenon pertains in the multiplicative noise setting and is robust with respect to certain perturbations of the irregular drift and of the small jumps of the noise.
"Generalized Peano problem with Lévy noise." Electron. Commun. Probab. 25 1 - 14, 2020. https://doi.org/10.1214/20-ECP365