Abstract

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