  The paper deals with strong global approximation of SDEs driven by two
independent processes: a nonhomogeneous Poisson process and a Wiener process.
We assume that the jump and diffusion coefficients of the underlying SDE
satisfy jump commutativity condition. We establish the exact convergence rate
of minimal errors that can be achieved by arbitrary algorithms based on a
finite number of observations of the Poisson and Wiener processes. We consider
classes of methods that use equidistant or nonequidistant sampling of the
Poisson and Wiener processes. We provide a construction of optimal methods,
based on the classical Milstein scheme, which asymptotically attain the
established minimal errors. The analysis implies that methods based on
nonequidistant mesh are more efficient than those based on the equidistant
mesh.
