On differentiability on initial data for solutions of stochastic equations with discontinuous coefficients

Stochastic differential equations with additive symmetric Levy stable noise with a parameter $\alpha\in(1;2]$ are considered. It is also assumed that the drift coefficient has a bounded variation. It is proved that a solution is Sobolev differentiable with respect to the initial value a.s., moreover, it generates a flow of homeomorphisms. The representation for the derivative is given.