A fractional stochastic differential equation with discontinuous diffusion driven by fBm with Hurst parameter less than 1∕2

The aim of this paper is to show the existence and uniqueness for the solution to a stochastic differential equation driven by fractional Brownian motion with Hurst parameter H<1∕2, with a discontinuous diffusion coefficient. The stochastic integral used in this paper is an extension of the Stratonovich integral introduced by León (Bernoulli 26 (2020) 2436–2462). In this way, we are able to complement previous results for SDEs driven by fBms with H>1∕2.