Stratonovich covariant differential equation with jumps

We study Stratonovich s.d.e. driven by semimartingales in the tangent bundle TM over a differentiable manifold MM. In ordinary differential geometry, a connection on MM is needed to define the covariant derivative of a C1C1 curve in TM; by the transfer principle, Elworthy and Norris have defined a Stratonovich covariant integration along a continuous semimartingale in TM. We extend this to the case when the semimartingale jumps, using Norris’s work and Cohen’s results on s.d.e. with jumps on manifolds, in order to give a discretization theorem for such Stratonovich covariant s.d.e. with jumps.