Stochastic equations with singular drift driven by fractional Brownian motion

We consider the stochastic differential equation dX<inf>t</inf> = b(X<inf>t</inf>) dt + dW^H<inf>t</inf>; where the drift b is either a measure or an integrable function, and W^H is a d-dimensional fractional Brownian motion with Hurst parameter (formula Presented) For the case where (formula Presented), we show weak existence of solutions to this equation under the condition d /p< 1/H -1^; which is an extension of the Krylov–Röckner condition (2005) to the fractional case. We construct a counterexample showing optimality of this condition. If b is a Radon measure, particularly the delta measure, we prove weak existence of solutions to this equation under the optimal condition (formula Presented) We also show strong well-posedness of solutions to this equation under certain conditions. To establish these results, we utilize the stochastic sewing technique and develop a new version of the stochastic sewing lemma.