On differentiability of stochastic flow for a multidimensional SDE with discontinuous drift

Abstract

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.

15 pages

References in corpus (3)

• Noise Prevents Singularities in Linear Transport Equations
• Absolute continuity under flows generated by SDE with measurable drift coefficient
• On properties of a flow generated by an SDE with discontinuous drift