Abstract

We study one-dimensional stochastic differential equations of the form dX(t) = sigma(X-t)dY(t), where Y is a suitable Holder continuous driver such as the fractional Brownian motion B-H with H > 1/2. The innovative aspect of the present paper lies in the assumptions on diffusion coefficients sigma for which we assume very mild conditions. In particular, we allow sigma to have discontinuities, and as such our results can be applied to study equations with discontinuous diffusions.