A numerical scheme for stochastic differential equations with distributional drift

In this paper we present a scheme for the numerical solution of one-dimensional stochastic differential equations (SDEs) whose drift belongs to fractional Sobolev space negative regularity (a subspace Schwartz distributions). We obtain rate convergence in suitable $L^1$-norm and implement numerically. To best our knowledge is first study (and implement) solutions SDEs lives distributions. As byproduct also an estimate applied with $L^p$-spaces $p\in(1,\infty)$.