Regularization of multiplicative SDEs through additive noise

We investigate the regularizing effect of certain additive continuous perturbations on SDEs with multiplicative fractional Brownian motion (fBm). Traditionally, a Lipschitz requirement drift and diffusion coefficients is imposed to ensure existence uniqueness SDE. show that suitable restore existence, regularity flow for resulting equation, even when both are distributional, thus extending program regularization by noise case SDEs. Our method relies combination nonlinear Young formalism developed Catellier Gubinelli (Stochastic Process. Appl. 126 (2016) 2323–2366), stochastic averaging estimates recently obtained Hairer Li (Ann. Probab. 48 (2020) 1826–1860).