Abstract

We study one-dimensional stochastic differential equations of the form dXt = ?(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 ? for which we assume very mild conditions. In particular, we allow ? to have discontinuities, and as such our results can be applied to study equations with discontinuous diffusions. © 2023 Taras Shevchenko National University of Kyiv