We consider a d-dimensional SDE with an identity diffusion matrix and a drift vector being a vector function of bounded variation. We give a representation for the derivative of the solution with respect to the initial data.
"On differentiability of stochastic flow for а multidimensional SDE with discontinuous drift." Electron. Commun. Probab. 19 1 - 17, 2014. https://doi.org/10.1214/ECP.v19-2886